A165809 a(n) = 3*n*(310*n^2 + 63*n - 12).

1083, 8124, 26703, 62400, 120795, 207468, 327999, 487968, 692955, 948540, 1260303, 1633824, 2074683, 2588460, 3180735, 3857088, 4623099, 5484348, 6446415, 7514880, 8695323, 9993324, 11414463, 12964320, 14648475, 16472508

Offset: 1

Author

A.K. Devaraj, Sep 29 2009

Keywords

• nonn
• easy

Comments

Old name was: Related to A165808; this sequence is that of rational integer coefficients of sqrt(-1) in the quotients f(x+k*f(x))/f(x) where f(x) = x^3 + 2x +11 and x = 2 +3i.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

GAP

List([1..35], n-> 3*n*(310*n^2 + 63*n - 12)); # G. C. Greubel, Sep 02 2019

Magma

[3*n*(310*n^2 + 63*n - 12): n in [1..35]]; // G. C. Greubel, Sep 02 2019

Maple

seq(3*n*(310*n^2 + 63*n - 12), n=1..35); # G. C. Greubel, Sep 02 2019

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1083, 8124, 26703, 62400}, 50] (* G. C. Greubel, Apr 09 2016 *)
Table[3n(310n^2+63n-12),{n,30}] (* Harvey P. Dale, Jun 15 2021 *)

PARI

a(n)=3*n*(310*n^2+63*n-12) \\ Charles R Greathouse IV, Jul 07 2013

Sage

[3*n*(310*n^2 + 63*n - 12) for n in (1..35)] # G. C. Greubel, Sep 02 2019

Formula

From R. J. Mathar, Sep 30 2009: (Start)

G.f.: 3*x*(361 + 1264*x + 235*x^2)/(1-x)^4.

a(n) = 3*n*(310*n^2 + 63*n - 12). (End)

From G. C. Greubel, Apr 09 2016: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

E.g.f.: 3*x*(361 + 993*x + 310*x^2)*exp(x). (End)

Extensions

More terms from R. J. Mathar, Sep 30 2009