Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Dec 28 2024 09:51:18
%S 1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627,792,
%T 1002,1255,1575,1958,2436,3010,3718,4565,5604,6842,8349,10143,12310,
%U 14883,17976,21635,26010,31175,37318,44547,53109,63153,74996,88850,105113,124078,146256,172032,202056,236844
%N a(n) is the number of partitions of n with Durfee square of size <= 5.
%H Andrew Howroyd, <a href="/A330643/b330643.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -2, -1, -2, 0, 2, 6, 2, -3, -6, -5, -2, 3, 12, 3, -2, -5, -6, -3, 2, 6, 2, 0, -2, -1, -2, 1, 2, -1).
%F a(n) = A000041(n), 0 <= n <= 35.
%F a(n) = A330642(n), 0 <= n <= 24.
%F a(n) = A330642(n) + A117487(n-24), n >= 25.
%F a(n) = n + A006918(n-3) + A117485(n) + A117486(n-16) + A117487(n-24), n >= 25.
%F G.f.: Sum_{k=0..5} x^(k^2)/(Product_{j=1..k} (1 - x^j))^2. - _Andrew Howroyd_, Dec 27 2024
%o (PARI) seq(n) = Vec(sum(k=0, 5, x^(k^2)/prod(j=1, k, 1 - x^j)^2) + O(x*x^n)) \\ _Andrew Howroyd_, Dec 27 2024
%Y Cf. A000041, A006918, A008805, A028310, A115994, A115720, A117485, A117486, A117487, A330640, A330641, A330642.
%K nonn
%O 0,3
%A _Omar E. Pol_, Dec 24 2019