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

Author

Paul Barry, Apr 02 2003

Keywords

• easy
• nonn

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

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

Crossrefs

Column k=4 of A082039.

Cf. A054569, A082040, A074377.

Programs

Mathematica

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

PARI

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

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)