OFFSET
1,1
COMMENTS
Binomial transform of 0, 4, 21, 18, 0, 0, 0, 0, ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, pp. 2211-2217.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 3*n^3 + 3*n^2/2 - n/2.
G.f.: x*(4 + 13*x + x^2) / (x-1)^4. (End)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 19 2012
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {4, 29, 93, 214}, 40] (* Vincenzo Librandi, Jun 19 2012 *)
Accumulate[Range[2, 121, 3]^2] (* Harvey P. Dale, Jun 24 2012 *)
PROG
(Magma) I:=[4, 29, 93, 214]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 19 2012
(PARI) a(n) = 3*n^3+n*(3*n-1)/2; \\ Altug Alkan, Sep 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved