A033571 a(n) = (2*n + 1)*(5*n + 1).

1, 18, 55, 112, 189, 286, 403, 540, 697, 874, 1071, 1288, 1525, 1782, 2059, 2356, 2673, 3010, 3367, 3744, 4141, 4558, 4995, 5452, 5929, 6426, 6943, 7480, 8037, 8614, 9211, 9828, 10465, 11122, 11799, 12496, 13213, 13950, 14707, 15484, 16281, 17098, 17935, 18792, 19669, 20566, 21483

Offset

0,2

Comments

Sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This is one of the diagonals in the spiral. - Omar E. Pol, Sep 10 2011

Also sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is a line perpendicular to the main axis A195015 in the same spiral. - Omar E. Pol, Oct 14 2011

Links

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

Leo Tavares, Illustration: Stellar Layers.

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

Formula

a(n) = A153126(2*n) = A000566(2*n+1). - Reinhard Zumkeller, Dec 20 2008

From Reinhard Zumkeller, Mar 13 2009: (Start)

a(n) = A008596(n) + A158186(n), for n > 0.

a(n) = A010010(n) - A158186(n). (End)

a(n) = a(n-1) + 20*n - 3 (with a(0)=1). - Vincenzo Librandi, Nov 17 2010

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

G.f.: (1 + 15*x + 4*x^2)/(1-x)^3.

E.g.f.: (1 + 17*x + 10*x^2)*exp(x). (End)

a(n) = A003154(n+1) + A007742(n). - Leo Tavares, Mar 27 2022

Sum_{n>=0} 1/a(n) = sqrt(1+2/sqrt(5))*Pi/6 + sqrt(5)*log(phi)/6 + 5*log(5)/12 - 2*log(2)/3, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 23 2022

Maple

seq((2*n+1)*(5*n+1), n=0..50); # G. C. Greubel, Oct 12 2019

Mathematica

Table[(2*n+1)*(5*n+1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)

Prog

(PARI) a(n)=(2*n+1)*(5*n+1) \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(2*n+1)*(5*n+1): n in [0..50]]; // G. C. Greubel, Oct 12 2019
(Sage) [(2*n+1)*(5*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n+1)*(5*n+1)); # G. C. Greubel, Oct 12 2019

Crossrefs

Cf. A153127. - Reinhard Zumkeller, Dec 20 2008

Cf. A000566, A008596, A010010, A153126, A158186.

Cf. A001622, A003154, A007742, A019952.

Sequence in context: A272138 A041630 A088593 * A041632 A086540 A041634

Adjacent sequences: A033568 A033569 A033570 * A033572 A033573 A033574

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

Terms a(36) onward added by G. C. Greubel, Oct 12 2019

Status

approved