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, 1030200, 1124760, 1224936

Offset

0,2

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

Paolo Xausa, Table of n, a(n) for n = 0..10000

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).

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

Maple

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

Mathematica

A054776[n_] := #*(#-1)*(#-2) & [3*n]; Array[A054776, 50, 0] (* Paolo Xausa, May 20 2026 *)

Prog

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

Crossrefs

Cf. A006566, A007531, A097321.

Sequence in context: A224303 A076233 A066581 * A076231 A076234 A066289

Adjacent sequences: A054773 A054774 A054775 * A054777 A054778 A054779

Keyword

easy,nonn

Author

Henry Bottomley, May 19 2000

Extensions

More terms from Paolo Xausa, May 20 2026

Status

approved