A005724 Coefficient of x^(3*n-1) and of x^(3*n+1) in the expansion of (1+x+x^2+x^3)^(2*n). (Formerly M3148)

3, 40, 546, 7728, 112035, 1650792, 24608948, 370084832, 5603730876, 85316186400, 1304770191802, 20029132137840, 308437355259930, 4762695514958640, 73716196036213800, 1143325208566357440, 17765127399780725316, 276484586847524844768, 4309270265307160983144

Offset

1,1

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..19.

R. K. Guy, Letter to N. J. A. Sloane, 1987

Formula

a(n) = A008287(2 * n, 3 * n - 1). - Sean A. Irvine, Aug 15 2016

Maple

seq(coeff((1+x+x^2+x^3)^(2*n), x, 3*n-1), n=1..30); # Robert Israel, Aug 15 2016

Crossrefs

Cf. A008287.

Sequence in context: A392533 A337692 A331795 * A215196 A093376 A019654

Adjacent sequences: A005721 A005722 A005723 * A005725 A005726 A005727

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed by Robert Israel, Aug 15 2016

New name from Mathew Englander, May 19 2026

Status

approved