A134062 Row sums of triangle A134061.

1, 8, 18, 38, 78, 158, 318, 638, 1278, 2558, 5118, 10238, 20478, 40958, 81918, 163838, 327678, 655358, 1310718, 2621438, 5242878, 10485758, 20971518, 41943038, 83886078, 167772158, 335544318, 671088638, 1342177278, 2684354558, 5368709118, 10737418238

Offset: 0

Author

Gary W. Adamson, Oct 05 2007

Keywords

• nonn
• easy

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,...).

Essentially the same as A131051 and A051633. - R. J. Mathar, Mar 28 2012

Examples

			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).
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A134061.

Programs

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 *)
LinearRecurrence[{3,-2},{1,8,18},40] (* Harvey P. Dale, Dec 17 2024 *)

PARI

Vec(-(4*x^2-5*x-1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Nov 17 2015

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)

Extensions

More terms from Jon E. Schoenfield, Jan 25 2015