[go: up one dir, main page]

login
A165809
a(n) = 3*n*(310*n^2 + 63*n - 12).
9
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
1,1
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.
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)
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 *)
PROG
(PARI) a(n)=3*n*(310*n^2+63*n-12) \\ Charles R Greathouse IV, Jul 07 2013
(Magma) [3*n*(310*n^2 + 63*n - 12): n in [1..35]]; // G. C. Greubel, Sep 02 2019
(Sage) [3*n*(310*n^2 + 63*n - 12) for n in (1..35)] # G. C. Greubel, Sep 02 2019
(GAP) List([1..35], n-> 3*n*(310*n^2 + 63*n - 12)); # G. C. Greubel, Sep 02 2019
CROSSREFS
Sequence in context: A221295 A220687 A188240 * A332069 A237804 A010091
KEYWORD
nonn,easy
AUTHOR
A.K. Devaraj, Sep 29 2009
EXTENSIONS
More terms from R. J. Mathar, Sep 30 2009
STATUS
approved