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# Name:Treasa Bency Biju Jose
# Date: 12-12-2020
# Assignment #24

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1. (i) nops(PnC(97, {1, 4, 5}, 7));
                             108236

(ii) nops(PnD(97, 3));
                             19990

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2. 
pnDC := proc(n, d, C, m) local k; 
seq(add(nops(PnkD(n, k, d) intersect PnkC(n, k, C, m)), k = 1 .. n)); 
end proc

(i) evalb(pnDC(10, 0, {1, 2}, 2) = pnC(10, {1, 2}, 2));
                              true

evalb(pnDC(10, 2, {0}, 1) = pnD(10, 2));
                              true

(ii) seq(pnDC(i, 0, {1}, 2), i = 1 .. 40);
1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 

  54, 64, 76, 89, 104, 122, 142, 165, 192, 222, 256, 296, 340, 

  390, 448, 512, 585, 668, 760, 864, 982, 1113


A-number := A000009

(iii) seq(pnDC(i, 2, {1, 4}, 5), i = 1 .. 40);
1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 3, 3, 2, 2, 3, 5, 5, 3, 3, 5, 7, 7, 6, 5, 
7, 11, 11, 8, 8, 12, 15, 15, 13, 12, 16, 22

A-number := A203776


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