A005892 Truncated square numbers: 7*n^2 + 4*n + 1. (Formerly M4833)

1, 12, 37, 76, 129, 196, 277, 372, 481, 604, 741, 892, 1057, 1236, 1429, 1636, 1857, 2092, 2341, 2604, 2881, 3172, 3477, 3796, 4129, 4476, 4837, 5212, 5601, 6004, 6421, 6852, 7297, 7756, 8229, 8716, 9217, 9732, 10261, 10804, 11361, 11932

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

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

Formula

a(n) = a(n-1) + 14*n - 3 (with a(0)=1). - Vincenzo Librandi, Nov 18 2010

From G. C. Greubel, Nov 30 2017: (Start)

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

G.f.: (1 + 9*x + 4*x^2)/(1 - x)^3.

E.g.f.: (1 + 11*x + 7*x^2)*exp(x). (End)

Maple

A005892:=-(1+9*z+4*z**2)/(z-1)**3; # Simon Plouffe in his 1992 dissertation

Mathematica

Table[7n^2+4n+1, {n, 0, 50}]  (* Harvey P. Dale, Mar 24 2011 *)

Prog

(PARI) a(n)=7*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [7*n^2 + 4*n + 1: n in [0..50]]; // G. C. Greubel, Nov 30 2017
(Sage) [7*n^2+4*n+1 for n in (0..50)] # G. C. Greubel, Apr 19 2019

Crossrefs

Cf. A135704.

Sequence in context: A045174 A044089 A044470 * A266398 A041276 A302884

Adjacent sequences: A005889 A005890 A005891 * A005893 A005894 A005895

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Frank Ellermann, Jan 18 2002

Status

approved