cp's OEIS Frontend

A330640 a(n) is the number of partitions of n with Durfee square of size <= 2.

%I A330640 #25 Jan 02 2020 09:53:39
%S A330640 1,1,2,3,5,7,11,15,22,29,40,51,67,83,105,127,156,185,222,259,305,351,
%T A330640 407,463,530,597,676,755,847,939,1045,1151,1272,1393,1530,1667,1821,
%U A330640 1975,2147,2319,2510,2701,2912,3123,3355,3587,3841,4095,4372,4649,4950,5251,5577,5903,6255,6607,6986
%N A330640 a(n) is the number of partitions of n with Durfee square of size <= 2.
%C A330640 This is an easy sequence since A006918 is the partial sums of A008805 (triangular numbers repeated).
%H A330640 Colin Barker, <a href="/A330640/b330640.txt">Table of n, a(n) for n = 0..1000</a>
%H A330640 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A330640 a(n) = A028310(n), 0 <= n <= 2.
%F A330640 a(n) = A028310(n) + A006918(n-3), n >= 3.
%F A330640 Or without A028310:
%F A330640 a(0) = 1, a(1) = 1, a(2) = 2.
%F A330640 a(n) = n + A006918(n-3), n >= 3.
%F A330640 From _Colin Barker_, Dec 31 2019: (Start)
%F A330640 G.f.: (1 - x - x^2 + 2*x^3 - x^5 + x^6) / ((1 - x)^4*(1 + x)^2).
%F A330640 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>6.
%F A330640 a(n) = (3 - 3*(-1)^n + (49+3*(-1)^n)*n - 6*n^2 + 2*n^3) / 48.
%F A330640 (End)
%o A330640 (PARI) Vec((1 - x - x^2 + 2*x^3 - x^5 + x^6) / ((1 - x)^4*(1 + x)^2) + O(x^60)) \\ _Colin Barker_, Dec 31 2019
%Y A330640 Cf. A000041, A006918, A008805, A028310, A115994, A115720.
%K A330640 nonn,easy
%O A330640 0,3
%A A330640 _Omar E. Pol_, Dec 22 2019