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A024862 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = floor( n/2 ), s = natural numbers, t = odd natural numbers. 2
3, 5, 17, 23, 50, 62, 110, 130, 205, 235, 343, 385, 532, 588, 780, 852, 1095, 1185, 1485, 1595, 1958, 2090, 2522, 2678, 3185, 3367, 3955, 4165, 4840, 5080, 5848, 6120, 6987, 7293, 8265, 8607, 9690, 10070, 11270, 11690, 13013, 13475, 14927, 15433, 17020, 17572, 19300 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

FORMULA

G.f.: x^2*(3+2*x+3*x^2) / ((1+x)^3*(x-1)^4). - R. J. Mathar, Sep 25 2013

a(n) = 3*A058187(n-2) +2*A058187(n-3)+3*A058187(n-4). - R. J. Mathar, Sep 25 2013

From Colin Barker, Jan 29 2016: (Start)

a(n) = (8*n^3+6*(-1)^n*n^2+12*n^2+6*(-1)^n*n-2*n+3*(-1)^n-3)/48.

a(n) = (4*n^3+9*n^2+2*n)/24 for n even.

a(n) = (4*n^3+3*n^2-4*n-3)/24 for n odd.

(End)

MATHEMATICA

CoefficientList[Series[(3 + 2 x + 3 x^2)/((1 + x)^3 (x - 1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 25 2013 *)

PROG

(PARI) Vec(x^2*(3+2*x+3*x^2)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 29 2016

CROSSREFS

Sequence in context: A100564 A231232 A154608 * A025106 A333199 A203193

Adjacent sequences:  A024859 A024860 A024861 * A024863 A024864 A024865

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified June 14 05:10 EDT 2021. Contains 345018 sequences. (Running on oeis4.)