A118979 O.g.f: -12*x^3/(-1+x)/(-1+2*x)/(-1+3*x) = -2-2/(-1+3*x)-6/(-1+x)+6/(-1+2*x) .

12, 72, 300, 1080, 3612, 11592, 36300, 111960, 342012, 1038312, 3139500, 9467640, 28501212, 85700232, 257493900, 773268120, 2321377212, 6967277352, 20908123500, 62736953400, 188236026012, 564758409672, 1694375892300

Offset: 3

Author

Roger L. Bagula, May 25 2006

Keywords

• nonn
• easy

Comments

Negative of the determinant of a series of 3 X 3 matrices, related to Stirling's numbers of the second kind by a factor of 12 (cf. A000392, A028243).

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A000392, A028243.

Programs

Mathematica

M = {{1, 1, 1}, {2^n, 4, 2}, {3^n, 9, 3}} a = Table[ -Det[M], {n, 3, 30}]

Formula

Let M = {{1, 1, 1}, {2^n, 4, 2}, {3^n, 9, 3}}. Then a(n) = -Det[M]

a(n) = 6*(1-2^n)+2*3^n = 12*A000392(n).

Extensions

Edited by N. J. A. Sloane, Dec 13 2007