A054776 a(n) = 3*n*(3*n-1)*(3*n-2).

0, 6, 120, 504, 1320, 2730, 4896, 7980, 12144, 17550, 24360, 32736, 42840, 54834, 68880, 85140, 103776, 124950, 148824, 175560, 205320, 238266, 274560, 314364, 357840, 405150, 456456, 511920, 571704, 635970, 704880, 778596, 857280, 941094

Offset: 0

Author

Henry Bottomley, May 19 2000

Keywords

• easy
• nonn

References

• L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 46.
• Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 268.

Links

• Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Crossrefs

Cf. A006566, A007531, A097321.

Programs

Maple

A054776:=n->3*n*(3*n-1)*(3*n-2): seq(A054776(n), n=0..50); # Wesley Ivan Hurt, Apr 14 2017

PARI

a(n)=3*n*(3*n-1)*(3*n-2)

Formula

a(n) = A007531(3n-2) = 6*A006566(n).

Sum_{n>=1} 1/a(n) = Pi*sqrt(3)/12 - log(3)/4 = 0.178796768891527... [Jolley eq. 250]. - Benoit Cloitre, Apr 05 2002

G.f.: 6*x*(1+16*x+10*x^2)/(1-x)^4.

E.g.f.: 3*exp(x)*x*(2 + 18x + 9x^2). - Indranil Ghosh, Apr 15 2017

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/3 - Pi/(6*sqrt(3)). - Amiram Eldar, Mar 08 2022