OFFSET
0,2
COMMENTS
a(n) = bottom term of the matrix-vector product M^n*V, where M = the 3 X 3 matrix [1,0,0; 0,1,0; 1,1,2] and V = [1,1,3].
Binomial transform of (1,7,3,7,3,7,3,...).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
For n > 0, a(n) = 5*2^n - 2. - Vaclav Kotesovec, Jan 26 2015
From Colin Barker, Nov 17 2015: (Start)
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
G.f.: -(4*x^2-5*x-1) / ((x-1)*(2*x-1)). (End)
EXAMPLE
a(2) = 18 = sum of row 2 terms, triangle A134061: (3 + 10 + 5).
a(3) = 38 = (1, 3, 3, 1) dot (1, 7, 3, 7) = (1 + 21 + 9 + 7).
MATHEMATICA
a=8; lst={1, a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
Flatten[{1, Table[5*2^n-2, {n, 1, 40}]}] (* Vaclav Kotesovec, Jan 26 2015 *)
PROG
(PARI) Vec(-(4*x^2-5*x-1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Nov 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Oct 05 2007
EXTENSIONS
More terms from Jon E. Schoenfield, Jan 25 2015
STATUS
approved