A024875 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = floor( n/2 ), s = natural numbers >= 3.

12, 15, 38, 45, 82, 94, 148, 166, 240, 265, 362, 395, 518, 560, 712, 764, 948, 1011, 1230, 1305, 1562, 1650, 1948, 2050, 2392, 2509, 2898, 3031, 3470, 3620, 4112, 4280, 4828, 5015, 5622, 5829, 6498, 6726, 7460, 7710, 8512, 8785, 9658, 9955, 10902, 11224, 12248, 12596

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[(12 + 3 x - 13 x^2 - 2 x^3 + 4 x^4)/((1 + x)^3 (x - 1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 25 2013 *)
LinearRecurrence[{1,3,-3,-3,3,1,-1},{12,15,38,45,82,94,148},50] (* Harvey P. Dale, Jul 21 2015 *)

PARI

Vec(x^2*(12+3*x-13*x^2-2*x^3+4*x^4)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 29 2016

Formula

G.f.: x^2*(12+3*x-13*x^2-2*x^3+4*x^4) / ((1+x)^3*(x-1)^4). - R. J. Mathar, Sep 25 2013

a(n) = 12*A058187(n-2) +3*A058187(n-3) -13*A058187(n-4) -2*A058187(n-5) +4*A058187(n-6). - R. J. Mathar, Sep 25 2013

From Colin Barker, Jan 29 2016: (Start)

a(n) = (4*n^3+3*((-1)^n+19)*n^2+2*(15*(-1)^n+61)*n+75*((-1)^n-1))/48.

a(n) = (2*n^3+30*n^2+76*n)/24 for n even.

a(n) = (2*n^3+27*n^2+46*n-75)/24 for n odd. (End)