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A288165
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Expansion of x^4/((1-x^4)*(1-x^3)*(1-x^6)*(1-x^9)).
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3
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 3, 2, 1, 5, 3, 2, 6, 5, 3, 9, 6, 5, 11, 9, 6, 15, 11, 9, 18, 15, 11, 23, 18, 15, 27, 23, 18, 34, 27, 23, 39, 34, 27, 47, 39, 34, 54, 47, 39, 64, 54, 47, 72, 64, 54, 84, 72, 64, 94, 84, 72, 108, 94, 84, 120, 108, 94, 136, 120
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OFFSET
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0,11
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0, -1, 0, 0, -1, 1, 0, 1, 1, 0, 0, -1).
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FORMULA
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a(n) = p_4(n/3) if n == 0 mod 3,
a(n) = p_4((n+8)/3) if n == 1 mod 3,
a(n) = p_4((n+4)/3) if n == 2 mod 3,
where p_4(n) is the number of partitions of n into exactly 4 parts.
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EXAMPLE
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a(57) = p_4(57/3) = p_4(19) = A001400(15) = 54,
a(58) = p_4((58+8)/3) = p_4(22) = A001400(18) = 84,
a(59) = p_4((59+4)/3) = p_4(21) = A001400(17) = 72,
a(60) = p_4(60/3) = p_4(20) = A001400(16) = 64,
a(61) = p_4((61+8)/3) = p_4(23) = A001400(19) = 94,
a(62) = p_4((62+4)/3) = p_4(22) = A001400(18) = 84.
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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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