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A152257 a(n) = (3^n - 1)^2*(3^n + 1)/16. 1
0, 1, 40, 1183, 32800, 893101, 24180520, 653473003, 17649155200, 476575627801, 12867977828200, 347439324082423, 9380897054183200, 253284538196972101, 6838685390919695080, 184644531291230453443, 4985402576490767372800, 134605871649898496094001 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = (3^n - 1)*(3^n - 1)*(3^n + 1)/16.
G.f.: x*(1-27*x^2)/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)). - Robert Israel, Mar 18 2019
a(n) = 40*a(n-1) - 390*a(n-2) + 1080*a(n-3) - 729*a(n-4) for n>3. - Colin Barker, Mar 18 2019
From G. C. Greubel, May 22 2023: (Start)
a(n) = A002452(n)*A003462(n).
a(n) = A007051(n)*A238976(n+1)/2.
E.g.f.: (1/16)*(exp(x) - exp(3*x) - exp(9*x) + exp(27*x)). (End)
MAPLE
seq((3^n-1)^2*(3^n+1)/16, n=0..30); # Robert Israel, Mar 18 2019
MATHEMATICA
Table[(9^n-1)*(3^n-1)/16, {n, 0, 30}]
PROG
(PARI) concat(0, Vec(x*(1 - 27*x^2) / ((1 - x)*(1 - 3*x)*(1 - 9*x)*(1 - 27*x)) + O(x^20))) \\ Colin Barker, Mar 18 2019
(Magma) [(9^n-1)*(3^n-1)/16: n in [0..40]]; // G. C. Greubel, May 22 2023
(SageMath) [(9^n-1)*(3^n-1)//16 for n in range(41)] # G. C. Greubel, May 22 2023
CROSSREFS
Sequence in context: A144914 A004385 A349596 * A229457 A331350 A061650
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Dec 01 2008
EXTENSIONS
0 inserted by Robert Israel, Mar 18 2019
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)