A204675 a(n) = 16*n^2 + 2*n + 1.

1, 19, 69, 151, 265, 411, 589, 799, 1041, 1315, 1621, 1959, 2329, 2731, 3165, 3631, 4129, 4659, 5221, 5815, 6441, 7099, 7789, 8511, 9265, 10051, 10869, 11719, 12601, 13515, 14461, 15439, 16449, 17491, 18565, 19671, 20809, 21979, 23181, 24415, 25681, 26979

Offset: 0

Author

Reinhard Zumkeller, Jan 18 2012

Keywords

• nonn
• easy

Comments

Central terms of the triangle A033293.

Also sequence found by reading the line from 1, in the direction 1, 19, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012

Links

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

Crossrefs

Cf. A017077, A033293, A074377, A136392.

Programs

Haskell

a204675 n = 2 * n * (8 * n + 1) + 1

Magma

I:=[1, 19, 69]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 19 2012

Mathematica

CoefficientList[Series[(1+x)*(1+15*x)/(1-x)^3,{x,0,50}],x] (* or *) LinearRecurrence[{3, -3, 1}, {1, 19, 69}, 50] (* Vincenzo Librandi, Mar 19 2012 *)

PARI

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

Formula

G.f.: (1+x)*(1+15*x)/(1-x)^3. - Bruno Berselli, Jan 18 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Jun 09 2023

E.g.f.: exp(x)*(1 + 2*x*(9 + 8*x)). - Elmo R. Oliveira, Oct 18 2024