A135703 a(n) = n*(7*n-2).

0, 5, 24, 57, 104, 165, 240, 329, 432, 549, 680, 825, 984, 1157, 1344, 1545, 1760, 1989, 2232, 2489, 2760, 3045, 3344, 3657, 3984, 4325, 4680, 5049, 5432, 5829, 6240, 6665, 7104, 7557, 8024, 8505, 9000, 9509, 10032, 10569, 11120, 11685, 12264, 12857, 13464

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

L. Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.

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

Formula

a(n) = 5*n + 14*binomial(n,2).

From R. J. Mathar, Apr 21 2008: (Start)

O.g.f. x*(5+9*x)/(1-x)^3.

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

a(n) = a(n-1) + 14*n - 9 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010

a(n) = 4*A000217(n) + A051624(n). - Bruno Berselli, Feb 11 2011

E.g.f.: x*(5 + 7*x)*exp(x). - G. C. Greubel, Oct 29 2016

Mathematica

Array[ #*(7*# - 2) &, 50, 0] (* Zerinvary Lajos, Jul 10 2009 *)

Prog

(PARI) a(n)=n*(7*n-2) \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [n*(7*n-2): n in [0..50]]; // G. C. Greubel, Jul 04 2019
(Sage) [n*(7*n-2) for n in (0..50)] # G. C. Greubel, Jul 04 2019
(GAP) List([0..50], n-> n*(7*n-2)) # G. C. Greubel, Jul 04 2019

Crossrefs

Cf. index to numbers of the form n*(d*n+10-d)/2 in A014106.

Cf. A185019.

Sequence in context: A202326 A085646 A121546 * A258290 A205669 A101147

Adjacent sequences: A135700 A135701 A135702 * A135704 A135705 A135706

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 04 2008

Status

approved