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A330640
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a(n) is the number of partitions of n with Durfee square of size <= 2.
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5
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1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 67, 83, 105, 127, 156, 185, 222, 259, 305, 351, 407, 463, 530, 597, 676, 755, 847, 939, 1045, 1151, 1272, 1393, 1530, 1667, 1821, 1975, 2147, 2319, 2510, 2701, 2912, 3123, 3355, 3587, 3841, 4095, 4372, 4649, 4950, 5251, 5577, 5903, 6255, 6607, 6986
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OFFSET
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0,3
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COMMENTS
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This is an easy sequence since A006918 is the partial sums of A008805 (triangular numbers repeated).
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LINKS
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FORMULA
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a(0) = 1, a(1) = 1, a(2) = 2.
G.f.: (1 - x - x^2 + 2*x^3 - x^5 + x^6) / ((1 - x)^4*(1 + x)^2).
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.
a(n) = (3 - 3*(-1)^n + (49+3*(-1)^n)*n - 6*n^2 + 2*n^3) / 48.
(End)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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