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A265645
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a(n) = n^2 * floor(n/2).
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4
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0, 0, 4, 9, 32, 50, 108, 147, 256, 324, 500, 605, 864, 1014, 1372, 1575, 2048, 2312, 2916, 3249, 4000, 4410, 5324, 5819, 6912, 7500, 8788, 9477, 10976, 11774, 13500, 14415, 16384, 17424, 19652, 20825, 23328, 24642, 27436, 28899, 32000, 33620, 37044, 38829, 42592, 44550, 48668, 50807, 55296, 57624, 62500
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x^2*(4 + 5*x + 11*x^2 + 3*x^3 + x^4)/((1 - x)^4*(1 + x)^3). - Ilya Gutkovskiy, Apr 14 2016; corrected by Colin Barker, Apr 14 2016
a(n) = n^2*(2*n + (-1)^n - 1)/4.
a(n) = n^3/2 for n even.
a(n) = n^2*(n-1)/2 for n odd.
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>6. (End)
Sum_{n>=2} 1/a(n) = zeta(3)/4 - Pi^2/4 - 2*log(2) + 4. - Amiram Eldar, Mar 15 2024
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MATHEMATICA
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LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {0, 0, 4, 9, 32, 50, 108}, 60] (* Harvey P. Dale, May 19 2019 *)
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PROG
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(Haskell)
seq' x = x^2 * (x `div` 2)
map seq' [0..50]
(PARI) concat(vector(2), Vec(x^2*(4+5*x+11*x^2+3*x^3+x^4)/((1-x)^4*(1+x)^3) + O(x^50))) \\ Colin Barker, Apr 14 2016
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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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