cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A035448 Number of partitions of n into parts 8k+1 or 8k+2.

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%I A035448 #13 Aug 03 2020 18:08:26
%S A035448 1,2,2,3,3,4,4,5,6,8,9,11,12,14,15,17,19,23,26,31,34,39,42,47,51,58,
%T A035448 65,74,82,92,100,110,119,132,145,163,179,199,216,237,255,279,303,334,
%U A035448 365,401,435,473,509,552,596,650,705,770,832,902,968,1044,1121,1213
%N A035448 Number of partitions of n into parts 8k+1 or 8k+2.
%H A035448 Robert Price, <a href="/A035448/b035448.txt">Table of n, a(n) for n = 1..1000</a>
%F A035448 a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(1/4) * Gamma(1/8) * 3^(1/16) / (8 * 2^(11/16) * Pi^(13/8) * n^(7/16)). - _Vaclav Kotesovec_, Aug 26 2015
%t A035448 nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+2))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%t A035448 nmax = 60; kmax = nmax/8;
%t A035448 s = Flatten[{Range[0, kmax]*8 + 1}~Join~{Range[0, kmax]*8 + 2}];
%t A035448 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 03 2020 *)
%Y A035448 Cf. A035679.
%K A035448 nonn
%O A035448 1,2
%A A035448 _Olivier Gérard_