A175109 a(n) = ((2*n+1)^3+(-1)^n)/2.

1, 13, 63, 171, 365, 665, 1099, 1687, 2457, 3429, 4631, 6083, 7813, 9841, 12195, 14895, 17969, 21437, 25327, 29659, 34461, 39753, 45563, 51911, 58825, 66325, 74439, 83187, 92597, 102689, 113491, 125023, 137313, 150381, 164255, 178955

Offset: 0

Author

R. J. Mathar, Feb 13 2010

Keywords

• easy
• nonn

Comments

Partial sums of A110907. Convolution of the finite sequence (1,10,26,10,1) with A002623.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A002623, A110907.

Programs

Magma

I:=[1, 13, 63, 171, 365]; [n le 5 select I[n] else 3*Self(n-1) - 2*Self(n-2) - 2*Self(n-3) + 3*Self(n-4) - Self(n-5): n in [1..40]]; // Vincenzo Librandi, Dec 19 2012

Maple

A175109:=n->((2*n+1)^3+(-1)^n)/2: seq(A175109(n), n=0..50); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

CoefficientList[Series[(x^2 + 4*x + 1)*(x^2 + 6*x + 1)/((1 + x)*(x - 1)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)

Formula

a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).

G.f.: (x^2+4*x+1)*(x^2+6*x+1)/((1+x)*(x-1)^4).