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.

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

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)

E.g.f.: (1/48)*(3*(1 - 4*x + 2*x^2)*exp(-x) + (-3 + 18*x + 36*x^2 + 8*x^3)*exp(x)). - G. C. Greubel, Apr 19 2023

Mathematica

CoefficientList[Series[(3+2x+3x^2)/((1+x)^3 (1-x)^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
(Magma) [((2*n-1)*(2*n+1)*(2*n+3) +3*(-1)^n*(n^2+(n+1)^2))/48: n in [2..50]]; // G. C. Greubel, Apr 19 2023
(SageMath) [((2*n-1)*(2*n+1)*(2*n+3) +3*(-1)^n*(n^2+(n+1)^2))/48 for n in range(2, 51)] # G. C. Greubel, Apr 19 2023

Crossrefs

Cf. A058187.

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