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 A218379 Number of partitions of n into pentagonal parts. 11

%I #27 Dec 09 2017 20:27:26

%S 1,1,1,1,1,2,2,2,2,2,3,3,4,4,4,5,5,6,6,6,7,7,9,9,10,11,11,13,13,14,15,

%T 15,17,17,19,21,22,24,24,26,28,29,31,31,34,36,38,41,42,45,47,50,53,54,

%U 57,59,63,67,69,73,76,80,84,87,91,94,99,103,107,112,118,124

%N Number of partitions of n into pentagonal parts.

%H Seiichi Manyama, <a href="/A218379/b218379.txt">Table of n, a(n) for n = 0..10000</a> (terms 1..100 from Antonio Roldán)

%e A(15)=5 because 15 = 12+1+1+1 = 5+5+5 = 5+5+1+1+1+1+1 = 5+1+1+1+1+1+1+1+1+1+1 = 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 with 12, 5, 1 pentagonal numbers.

%o (PARI) {for (n=1, 100,p=truncate((1+sqrt(24*n+1))/6);m=polcoeff(prod(k=1,p,q=(3*k-1)*k/2;sum(h=0,truncate(n/q+1),x^(h*q))),n);write("B218379.txt",n," ",m))}

%Y Cf. A000326, A095699.

%K nonn

%O 0,6

%A _Antonio Roldán_, Oct 27 2012

%E a(0) = 1 prepended by _Seiichi Manyama_, Dec 09 2017

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