A261893 a(n) = (n+1)^3 - n^2.

1, 7, 23, 55, 109, 191, 307, 463, 665, 919, 1231, 1607, 2053, 2575, 3179, 3871, 4657, 5543, 6535, 7639, 8861, 10207, 11683, 13295, 15049, 16951, 19007, 21223, 23605, 26159, 28891, 31807, 34913, 38215, 41719, 45431, 49357, 53503, 57875, 62479, 67321, 72407

Offset: 0

Author

Reinhard Zumkeller, Sep 05 2015

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000290, A000578.

Subsequence of A167222.

Programs

Haskell

a261893 n = n * (n * (n + 2) + 3) + 1
a261893_list = zipWith (-) (tail a000578_list) a000290_list

Magma

[n^3+2*n^2+3*n+1: n in [0..50]]; // Bruno Berselli, Jul 04 2016

Mathematica

Table[n^3 + 2 n^2 + 3 n + 1, {n, 0, 50}] (* Bruno Berselli, Jul 04 2016 *)
LinearRecurrence[{4,-6,4,-1},{1,7,23,55},50] (* Harvey P. Dale, Mar 01 2023 *)

Maxima

makelist(n^3+2*n^2+3*n+1, n, 0, 50); /* Bruno Berselli, Jul 04 2016 */

PARI

vector(50, n, n--; n^3+2*n^2+3*n+1) \\ Bruno Berselli, Jul 04 2016

Sage

[n^3+2*n^2+3*n+1 for n in range(50)]; # Bruno Berselli, Jul 04 2016

Formula

a(n) = n^3 + 2*n^2 + 3*n + 1.

a(n) = A000578(n+1) - A000290(n).

O.g.f.: (1 + 3*x + x^2 + x^3)/(1 - x)^4. - Bruno Berselli, Jul 04 2016

E.g.f.: (1 + 6*x + 5*x^2 + x^3)*exp(x). - Bruno Berselli, Jul 04 2016