OFFSET
1,1
COMMENTS
The recursive multipliers (9), (-26), (24) are present with changed signs in the characteristic polynomial of M: x^3 - 9x^2 + 26x - 24.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-26,24).
FORMULA
a(n+3) = 9*a(n+2) - 26*a(n+1) + 24*a(n), a(1) = 2, a(2) = 31, a(3) = 137. Let M = the 3 X 3 matrix [2 0 0 / 3 3 0 / 4 6 4] (derived from Pascal's triangle rows by deleting the 1's and filling in with 0's). Then M^n * [1 0 0] = [2^n 3*A001047(n) 2*A095262(n)].
From Colin Barker, Oct 21 2012: (Start)
a(n) = (7*2^n-2*3^(2+n)+11*4^n)/2.
G.f.: -x*(3*x+2)/((2*x-1)*(3*x-1)*(4*x-1)). (End)
EXAMPLE
MATHEMATICA
a[n_] := (MatrixPower[{{2, 0, 0}, {3, 3, 0}, {4, 6, 4}}, n].{{1}, {0}, {0}})[[3, 1]]/2; Table[ a[n], {n, 22}] (* Robert G. Wilson v, Jun 05 2004 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, May 31 2004
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Jun 05 2004
STATUS
approved