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2, 5, 11, 18, 29, 43, 61, 84, 111, 145, 183, 230, 281, 343, 409, 488, 571, 669, 771, 890, 1013, 1155, 1301, 1468, 1639, 1833, 2031, 2254, 2481, 2735, 2993, 3280, 3571, 3893, 4219, 4578, 4941, 5339, 5741, 6180, 6623, 7105, 7591, 8118, 8649, 9223, 9801, 10424
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OFFSET
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1,1
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LINKS
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FORMULA
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Let g = n + ((n + 1) mod 2), then for n > 1,
a(n) = (g^3 + 6*g^2 + 11*g + 18) / 12 - If(n mod 2 = 1, 0, ((n + 2) / 2)^2 + 2).
G.f.: x*(2 + x - x^2 - x^3 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)^2).
a(n) = (n^3 + 6*n^2 + 14*n) / 12 for n>1 and even.
a(n) = (n^3 + 6*n^2 + 11*n + 18) / 12 for n>1 and odd.
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.
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EXAMPLE
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For n = 5 then a(5) = 2+3+6+7+11 = 29.
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MATHEMATICA
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CoefficientList[ Series[(2 + x - x^2 - x^3 + 2x^5 - x^6)/((x -1)^4 (x + 1)^2), {x, 0, 50}], x] (* Robert G. Wilson v, Jan 18 2018 *)
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PROG
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(PARI) Vec(x*(2 + x - x^2 - x^3 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Jan 18 2018
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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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