A134067 Row sums of triangle A134066.

1, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, 536870910, 1073741822, 2147483646, 4294967294, 8589934590, 17179869182

Offset: 0

Author

Gary W. Adamson, Oct 06 2007

Keywords

• nonn
• easy

Comments

Essentially the same as A095121. - R. J. Mathar, Mar 28 2012

Examples

			a(3) = 30 = sum of row 3 terms of triangle A134066: (2 + 12 + 12 + 4).
a(3) = 30 = (1, 3, 3, 1) dot (1, 5, 3, 5) = (1 + 15 + 9 + 5).
		

Links

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

Crossrefs

Cf. A095121, A134066.

Programs

Mathematica

Join[{1}, LinearRecurrence[{3, -2}, {6, 14}, 50]] (* Vladimir Joseph Stephan Orlovsky, Feb 23 2012 *)

PARI

Vec(-(2*x^2-3*x-1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 13 2014

Formula

Binomial transform of (1, 5, 3, 5, 3, 5, ...).

From Colin Barker, Mar 13 2014: (Start)

a(n) = 2^(2+n) - 2 for n > 0.

a(n) = 3*a(n-1) - 2*a(n-2) for n > 0.

G.f.: -(2*x^2-3*x-1) / ((x-1)*(2*x-1)). (End)

E.g.f.: 2*exp(x)*(2*exp(x) - 1) - 1. - Stefano Spezia, May 07 2023