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
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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
MATHEMATICA
LinearRecurrence[{8, -19, 12}, {1, 1, 2}, 30] (* Harvey P. Dale, Jul 07 2024 *)
CROSSREFS
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