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
Examples
a(4) = 31 = (1, 3, 3, 1) dot (1, 3, 7, 0) = (1 + 9 + 21 + 0).
Links
- Derek Kinsella, Plane division by lines and circles. [Wayback Machine link]
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 265, 7}]; lst (* Zerinvary Lajos, Jul 11 2009 *) -
PARI
a(n)=n*(7*n-15)/2+5 \\ Charles R Greathouse IV, Jun 17 2017
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
Extensions
More terms from R. J. Mathar, May 06 2008