A140063 Binomial transform of [1, 3, 7, 0, 0, 0, ...].

1, 4, 14, 31, 55, 86, 124, 169, 221, 280, 346, 419, 499, 586, 680, 781, 889, 1004, 1126, 1255, 1391, 1534, 1684, 1841, 2005, 2176, 2354, 2539, 2731, 2930, 3136, 3349, 3569, 3796, 4030, 4271, 4519, 4774, 5036

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Derek Kinsella, Plane division by lines and circles

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

Formula

A007318 * [1, 3, 7, 0, 0, 0, ...].

O.g.f.: x*(1 + x + 5x^2)/(1-x)^3. - R. J. Mathar, May 06 2008

a(n) = 7*n^2/2 - 15*n/2 + 5 = 3*a(n-1) - 3*a(n-2) + a(n-3). - R. J. Mathar, Jul 31 2009

a(n) = a(n-1) + 7*n - 11 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010

Example

a(4) = 31 = (1, 3, 3, 1) dot (1, 3, 7, 0) = (1 + 9 + 21 + 0).

Mathematica

s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 265, 7}]; lst # Zerinvary Lajos, Jul 11 2009

Prog

(PARI) a(n)=n*(7*n-15)/2+5 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A079776 A117109 A317031 * A051409 A072475 A001740

Adjacent sequences: A140060 A140061 A140062 * A140064 A140065 A140066

Keyword

nonn,easy

Author

Gary W. Adamson, May 03 2008

Extensions

More terms from R. J. Mathar, May 06 2008

Status

approved