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a(n) is the number of partitions of n with Durfee square of size <= 2.
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%I #25 Jan 02 2020 09:53:39

%S 1,1,2,3,5,7,11,15,22,29,40,51,67,83,105,127,156,185,222,259,305,351,

%T 407,463,530,597,676,755,847,939,1045,1151,1272,1393,1530,1667,1821,

%U 1975,2147,2319,2510,2701,2912,3123,3355,3587,3841,4095,4372,4649,4950,5251,5577,5903,6255,6607,6986

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

%C This is an easy sequence since A006918 is the partial sums of A008805 (triangular numbers repeated).

%H Colin Barker, <a href="/A330640/b330640.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

%F a(n) = A028310(n), 0 <= n <= 2.

%F a(n) = A028310(n) + A006918(n-3), n >= 3.

%F Or without A028310:

%F a(0) = 1, a(1) = 1, a(2) = 2.

%F a(n) = n + A006918(n-3), n >= 3.

%F From _Colin Barker_, Dec 31 2019: (Start)

%F G.f.: (1 - x - x^2 + 2*x^3 - x^5 + x^6) / ((1 - x)^4*(1 + x)^2).

%F 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 a(n) = (3 - 3*(-1)^n + (49+3*(-1)^n)*n - 6*n^2 + 2*n^3) / 48.

%F (End)

%o (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 Cf. A000041, A006918, A008805, A028310, A115994, A115720.

%K nonn,easy

%O 0,3

%A _Omar E. Pol_, Dec 22 2019