A033572 a(n) = (2*n+1)*(7*n+1).

1, 24, 75, 154, 261, 396, 559, 750, 969, 1216, 1491, 1794, 2125, 2484, 2871, 3286, 3729, 4200, 4699, 5226, 5781, 6364, 6975, 7614, 8281, 8976, 9699, 10450, 11229, 12036, 12871, 13734, 14625, 15544, 16491, 17466, 18469, 19500, 20559, 21646, 22761, 23904, 25075, 26274, 27501, 28756

Offset

0,2

Comments

Sequence found by reading the line from 1, in the direction 1, 24,..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Also sequence found by reading the same line in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 13 2011

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) + 28*n - 5 for n>0, a(0)=1. - Vincenzo Librandi, Nov 17 2010

From G. C. Greubel, Oct 12 2019: (Start)

G.f.: (1 + 21*x + 6*x^2)/(1-x)^3.

E.g.f.: (1 + 23*x + 14*x^2)*exp(x). (End)

Sum 1/a(n) = -gamma/5 -2*log(2)/5 -psi(1/7)/5 = 1.0800940432405839438217..., gamma=A001620, psi(1/7) = -A354627. - R. J. Mathar, May 07 2024

Maple

seq((2*n+1)*(7*n+1), n=0..50); # G. C. Greubel, Oct 12 2019

Mathematica

Table[(2*n+1)*(7*n+1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)
LinearRecurrence[{3, -3, 1}, {1, 24, 75}, 50] (* Harvey P. Dale, Apr 19 2023 *)

Prog

(PARI) a(n)=(2*n+1)*(7*n+1) \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(2*n+1)*(7*n+1): n in [0..50]] # G. C. Greubel, Oct 12 2019
(Sage) [(2*n+1)*(7*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n+1)*(7*n+1)); # G. C. Greubel, Oct 12 2019

Crossrefs

Bisection of A001106.

Sequence in context: A185940 A378065 A265424 * A233883 A291630 A195027

Adjacent sequences: A033569 A033570 A033571 * A033573 A033574 A033575

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved