A296363 a(1)=0; for n>1, a(n) = 4*n^3 - 3*n^2 - 3*n + 4.

0, 18, 76, 200, 414, 742, 1208, 1836, 2650, 3674, 4932, 6448, 8246, 10350, 12784, 15572, 18738, 22306, 26300, 30744, 35662, 41078, 47016, 53500, 60554, 68202, 76468, 85376, 94950, 105214, 116192, 127908, 140386, 153650, 167724, 182632, 198398, 215046, 232600

Offset: 1

Author

N. J. A. Sloane, Dec 16 2017

Keywords

• nonn
• easy

Comments

This was once thought (mistakenly) to be a formula for A262402.

Links

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

Crossrefs

Cf. A262402.

Programs

Magma

[0] cat [4*n^3-3*n^2-3*n+4: n in [2..40]]; // Vincenzo Librandi, Sep 23 2015

Mathematica

CoefficientList[Series[- 2 x (x^3 - 2 x^2 - 2 x - 9)/(x - 1)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Sep 23 2015 *)
Join[{0},LinearRecurrence[{4, -6, 4, -1},{18, 76, 200, 414},38]] (* Ray Chandler, Sep 23 2015 *)
Join[{0},Table[4n^3-3n^2-3n+4,{n,2,40}]] (* Harvey P. Dale, Mar 28 2019 *)

PARI

a(n)=if(n>1, 4*n^3 - 3*n^2 - 3*n + 4, 0) \\ Charles R Greathouse IV, Oct 18 2022

Formula

G.f.: -2 * (x^3-2*x^2-2*x-9) * x^2 / (x-1)^4.