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# Name:Treasa Bency Biju Jose
# Date: 10-30-2020
# Assignment #15
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1.
RoG := proc(k, n) local V, E, i, j, T1, v, Neighs, Moves, m, pt; 
V := [seq(seq(seq([i, j], j = 1 .. n), i = 1 .. k))]; 
for i to nops(V) do 
	T1[V[i]] := i; 
end do; E := []; 
for i to nops(V) do 
	pt := V[i]; 
	Moves := {[-3, 0], [-2, 0], [-1, 0], [0, -3], [0, -2], [0, -1], [0, 1], [0, 2], [0, 3], 
	[0, 4], [1, 0], [2, 0], [3, 0], [4, 0]}; 
	Neighs := {seq(pt + m, m in Moves)}; 
	Neighs := Neighs intersect convert(V, set); 
	E := [op(E), {seq(T1[v], v in Neighs)}]; 
end do; 
E, V; 
end proc;

seq(SAWnu(RoG(3, n)[1]), n = 1 .. 7);
           2, 6, 96, 3132, 176688, 6042500, 175997224

This sequence is not on OEIS

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2. 
# ComboProject2

SeqW({[0, 1], [1, 0], [1, 1], [2, 2]}, 40);
[3, 14, 71, 379, 2082, 11651, 66051, 378064, 2180037, 12644861, 

  73695358, 431209313, 2531556197, 14904832196, 87970766447, 

  520337606401, 3083584244460, 18304476242735, 108820740004749, 

  647817646760368, 3861215365595659, 23039691494489015, 

  137615812845579390, 822738993163308691, 4922949521986023963, 

  29480139394909356044, 176664398792213185409, 

  1059402929496079389631, 6356902648489583020308, 

  38166637970127629445209, 229276573792993574603787, 

  1378027658578343598968422, 8286384291210047832045023, 

  49850407222197537838691609, 300025068023888975708739560, 

  1806430285705003018542769435, 10880533315007764522316552713, 

  65559512416370766384694103782, 395157036800184178672318869369, 

  2382564832244243056285491057263]


SeqGW({[0, 1], [1, 0], [1, 1], [2, 2]}, 40);
[2, 7, 27, 116, 532, 2554, 12675, 64507, 334836, 1765833, 

  9434779, 50962640, 277839361, 1526834471, 8448751385, 

  47035469902, 263260232668, 1480527858436, 8361881707770, 

  47409359120684, 269736194796537, 1539547726712437, 

  8812663513352489, 50579825742416942, 291012706492224315, 

  1678146650028389023, 9697482307486861125, 56148049483650883418, 

  325685956663306169704, 1892343209238706561552, 

  11012606961635116334631, 64184027732131247229285, 

  374603199042488986947084, 2189213854778309191457243, 

  12809866709764967142650533, 75043134255268720569687608, 

  440108608055424139245905601, 2583842686807144572684013803, 

  15184702028756125034970193936, 89322096703094945357683861273]


#ComboProject3

SeqW({[0, 0, 1], [0, 1, 0], [1, 0, 0], [1, 1, 1]}, 20);
[7, 115, 2371, 54091, 1307377, 32803219, 844910395, 22188235867, 

  591446519797, 15953338537885, 434479441772845, 

  11927609772412075, 329653844941016785, 9163407745486783435, 

  255982736410338609931, 7181987671728091545787, 

  202271071826031620236525, 5715984422606794841997001, 

  162016571360163769411597081, 4604748196249289767697705221]


SeqGW({[0, 0, 1], [0, 1, 0], [1, 0, 0], [1, 1, 1]}, 20);
[2, 10, 88, 1043, 14778, 236001, 4107925, 76314975, 1491934038, 

  30389576308, 640286048416, 13877540824735, 308102204007536, 

  6983346070924707, 161156356282624227, 3778249609096250059, 

  89826197363219012470, 2162338803354415120414, 

  52637415804379149938876, 1294313658632145337351381]



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