A010021 a(0) = 1, a(n) = 32*n^2 + 2 for n > 0.

1, 34, 130, 290, 514, 802, 1154, 1570, 2050, 2594, 3202, 3874, 4610, 5410, 6274, 7202, 8194, 9250, 10370, 11554, 12802, 14114, 15490, 16930, 18434, 20002, 21634, 23330, 25090, 26914, 28802, 30754, 32770, 34850, 36994, 39202, 41474, 43810, 46210, 48674, 51202

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

From Omar E. Pol, Apr 21 2021: (Start)

Sequence found by reading the line segment from 1 to 34 together with the line from 34, in the direction 34, 130, ..., in the rectangular spiral whose vertices are the generalized 18-gonal numbers A274979.

The spiral begins as follows:

46_ _ _ _ _ _ _ _ _ _18

| |

| 0 |

| | _ _ _ _ |

| 1 15

|

51

(End)

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A206399, A158563, A158575, A244082.

Cf. A274979 (generalized 18-gonal numbers).

Programs

Mathematica

Join[{1}, 32 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
CoefficientList[Series[(1 + x) (1 + 30 x + x^2)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 25 2014 *)

Formula

G.f.: (1+x)*(1+30*x+x^2)/(1-x)^3. [Bruno Berselli, Feb 07 2012]

a(n) = A005893(4n) = A008527(2n); a(n+1) = A108100(2n+2). [Bruno Berselli, Feb 07 2012]

E.g.f.: (x*(x+1)*32+2)*e^x-1. - Gopinath A. R., Feb 14 2012

a(n) = (4n+1)^2+(4n-1)^2 for n>0. [Bruno Berselli, Jun 24 2014]

a(n) = A244082(n) + 2, n >= 1. - Omar E. Pol, Apr 21 2021

Sum_{n>=0} 1/a(n) = 3/4 + Pi/16*coth(Pi/4) = 1.04940725316131.. - R. J. Mathar, May 07 2024

a(n) = 2*A108211(n). - R. J. Mathar, May 07 2024

a(n) = A195315(n)+A195315(n+1). - R. J. Mathar, May 07 2024