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Number of partitions of n into distinct generalized heptagonal numbers (A085787).
2

%I #6 Feb 16 2025 08:33:51

%S 1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,1,2,1,1,1,1,1,1,2,1,1,1,1,1,2,2,0,

%T 2,3,1,0,3,3,1,2,2,1,1,3,3,3,2,1,2,3,4,3,2,2,3,3,3,5,3,1,3,4,3,4,5,2,

%U 3,5,4,3,4,5,4,4,3,5,5,3,5,7,5,3,6,6,6,6,5,5,6,6,5,8,7,5,5,6,7,8,8

%N Number of partitions of n into distinct generalized heptagonal numbers (A085787).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} (1 + x^(k*(5*k-3)/2))*(1 + x^(k*(5*k+3)/2)).

%e a(18) = 2 because we have [18] and [13, 4, 1].

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(k (5 k - 3)/2)) (1 + x^(k (5 k + 3)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A024940, A085787, A279280, A290942, A294621, A294624.

%K nonn,changed

%O 0,19

%A _Ilya Gutkovskiy_, Nov 05 2017