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A204674
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a(n) = 4*n^3 + 5*n^2 + 2*n + 1.
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6
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1, 12, 57, 160, 345, 636, 1057, 1632, 2385, 3340, 4521, 5952, 7657, 9660, 11985, 14656, 17697, 21132, 24985, 29280, 34041, 39292, 45057, 51360, 58225, 65676, 73737, 82432, 91785, 101820, 112561, 124032, 136257, 149260, 163065, 177696, 193177, 209532, 226785, 244960, 264081
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history;
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internal format)
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OFFSET
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0,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = (4*n^2 + n + 1) * (n + 1).
G.f.: (1 + 3*x)*(1 + 5*x)/(1 - x)^4. - Andrew Howroyd, Jan 07 2020
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {1, 12, 57, 160}, 50] (* or *) CoefficientList[ Series[(1+3x)(1+5x)/(1-x)^4, {x, 0, 50}], x] (* Harvey P. Dale, Jun 25 2021 *)
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PROG
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(Haskell)
a204674 n = n * (n * (4 * n + 5) + 2) + 1
(PARI) a(n)={ 4*n^3 + 5*n^2 + 2*n + 1 } \\ Andrew Howroyd, Jan 07 2020
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CROSSREFS
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Row sums of A033293.
Cf. A054567, A226449.
Sequence in context: A224832 A139256 A166997 * A123983 A212682 A212134
Adjacent sequences: A204671 A204672 A204673 * A204675 A204676 A204677
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KEYWORD
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nonn,easy
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AUTHOR
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Reinhard Zumkeller, Jan 18 2012
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EXTENSIONS
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Terms a(26) and beyond from Andrew Howroyd, Jan 07 2020
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STATUS
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approved
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