A024869 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 >= 2, t = natural numbers >= 3.

8, 10, 27, 32, 61, 70, 114, 128, 190, 210, 293, 320, 427, 462, 596, 640, 804, 858, 1055, 1120, 1353, 1430, 1702, 1792, 2106, 2210, 2569, 2688, 3095, 3230, 3688, 3840, 4352, 4522, 5091, 5280, 5909, 6118, 6810, 7040, 7798, 8050, 8877, 9152, 10051, 10350, 11324, 11648

Offset: 2

Author

Clark Kimberling

Keywords

• nonn
• easy

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)

Programs

Mathematica

CoefficientList[Series[(8 + 2 x - 7 x^2 - x^3 + 2 x^4)/((1 + x)^3 (x - 1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 25 2013 *)

PARI

Vec(x^2*(8+2*x-7*x^2-x^3+2*x^4)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 29 2016

Formula

G.f.: x^2*(8+2*x-7*x^2-x^3+2*x^4) / ((1+x)^3*(x-1)^4). - R. J. Mathar, Sep 25 2013

a(n) = 8*A058187(n-2) +2*A058187(n-3) -7*A058187(n-4) -A058187(n-5) +2*A058187(n-6). - R. J. Mathar, Sep 25 2013

From Colin Barker, Jan 29 2016: (Start)

a(n) = (4*n^3+3*((-1)^n+13)*n^2+4*(6*(-1)^n+17)*n+42*((-1)^n-1))/48.

a(n) = (2*n^3+21*n^2+46*n)/24 for n even.

a(n) = (2*n^3+18*n^2+22*n-42)/24 for n odd.

(End)