A239449 a(n) = 7*n^2 - 5*n + 1.

1, 3, 19, 49, 93, 151, 223, 309, 409, 523, 651, 793, 949, 1119, 1303, 1501, 1713, 1939, 2179, 2433, 2701, 2983, 3279, 3589, 3913, 4251, 4603, 4969, 5349, 5743, 6151, 6573, 7009, 7459, 7923, 8401, 8893, 9399, 9919, 10453, 11001, 11563, 12139, 12729, 13333, 13951

Offset: 0

Author

Reinhard Zumkeller, Mar 19 2014

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A003215, A239426.

Programs

Haskell

a239449 n = (7 * n - 5) * n + 1

Magma

[7*n^2-5*n+1: n in [0..50]]; // Vincenzo Librandi, Apr 02 2014

Mathematica

CoefficientList[Series[(1 + 13 x^2)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 02 2014 *)

PARI

a(n)=7*n^2-5*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = A239426(n)/A003215(n-1).

G.f.: (-1-13*x^2)/(x-1)^3. - R. J. Mathar, Mar 31 2014

From Elmo R. Oliveira, Nov 16 2024: (Start)

E.g.f.: exp(x)*(1 + 2*x + 7*x^2).

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