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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Bisection of A001106.

Programs

GAP

List([0..50], n-> (2*n+1)*(7*n+1)); # G. C. Greubel, Oct 12 2019

Magma

[(2*n+1)*(7*n+1): n in [0..50]]; // G. C. Greubel, Oct 12 2019

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 *)

PARI

a(n)=(2*n+1)*(7*n+1) \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(2*n+1)*(7*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019

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