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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A017077, A033293, A074377, A136392.

Sequence in context: A044538 A297226 A300463 * A007546 A007547 A217081

Adjacent sequences: A204672 A204673 A204674 * A204676 A204677 A204678

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 18 2012

Status

approved