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

0,2

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A095121, A134066.

Sequence in context: A183023 A284246 A210000 * A350107 A024932 A273365

Adjacent sequences: A134064 A134065 A134066 * A134068 A134069 A134070

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 06 2007

Status

approved