A162725 a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) (n >= 3) with a(0) = a(1) = 1, a(2) = 2.

1, 1, 2, 9, 46, 221, 1002, 4369, 18566, 77541, 320002, 1309529, 5326686, 21572461, 87087002, 350739489, 1410132406, 5662052981, 22712782002, 91044838249, 364760483726, 1460785327101, 5848371485002, 23409176469809, 93683777468646

Offset

0,3

Comments

The above sequence also satisfies a(n) - 7*a(n-1) + 12*a(n-2) = 7 (n >= 2) with a(0)=a(1)=1.

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

a(n) = 4^n/3 - 3^n/2 + 7/6. - Emeric Deutsch, Jul 19 2009

G.f.: -(1-7*x+13*x^2)/((x-1)*(3*x-1)*(4*x-1)). - R. J. Mathar, Jul 31 2009

Maple

seq(7/6-(1/2)*3^n+(1/3)*4^n, n = 0 .. 25); # Emeric Deutsch, Jul 19 2009

Crossrefs

Sequence in context: A228767 A074607 A251178 * A268171 A168431 A036726

Adjacent sequences: A162722 A162723 A162724 * A162726 A162727 A162728

Keyword

nonn,easy

Author

Tian-Xiao He (the(AT)iwu.edu), Jul 11 2009

Extensions

More terms from Vincenzo Librandi, Jul 13 2009

Extended by Emeric Deutsch, Jul 19 2009

Status

approved