A082041 a(n) = 16*n^2 + 4*n + 1.

1, 21, 73, 157, 273, 421, 601, 813, 1057, 1333, 1641, 1981, 2353, 2757, 3193, 3661, 4161, 4693, 5257, 5853, 6481, 7141, 7833, 8557, 9313, 10101, 10921, 11773, 12657, 13573, 14521, 15501, 16513, 17557, 18633, 19741, 20881, 22053, 23257, 24493

Offset

0,2

Comments

Also sequence found by reading the segment (1,21) together with the line from 21, in the direction 21, 73, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012

Links

Table of n, a(n) for n=0..39.

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

Formula

G.f.: (-1-18*x-13*x^2)/(x-1)^3 . - R. J. Mathar, Dec 03 2014

From Elmo R. Oliveira, Oct 28 2024: (Start)

E.g.f.: exp(x)*(1 + 20*x + 16*x^2).

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

Mathematica

Table[16n^2+4n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 21, 73}, 50] (* Harvey P. Dale, Sep 28 2024 *)

Prog

(PARI) a(n)=16*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Column k=4 of A082039.

Cf. A054569, A082040, A074377.

Sequence in context: A240824 A109357 A283802 * A350160 A316887 A296155

Adjacent sequences: A082038 A082039 A082040 * A082042 A082043 A082044

Keyword

easy,nonn

Author

Paul Barry, Apr 02 2003

Status

approved