A131056 A007318 * A131055.

1, 3, 7, 17, 41, 97, 225, 513, 1153, 2561, 5633, 12289, 26625, 57345, 122881, 262145, 557057, 1179649, 2490369, 5242881, 11010049, 23068673, 48234497, 100663297, 209715201, 436207617, 905969665

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-8,4)

Formula

Binomial transform of A131055: (1, 2, 2, 4, 4, 6, 6, ...). A131056 = A131054 as an infinite lower triangular matrix * [1,2,3,...] as a vector.

G.f.: x*(1-2*x+2*x^3)/((1-x)*(1-2*x)^2); a(n)=-0^n/2+2^(n-1)*(n+1)+1. - Paul Barry, Jun 14 2008

a(n) = 2+A099035(n-1), n>1. - Juri-Stepan Gerasimov, Oct 02 2011

Example

a(4) = 17 = (1, 3, 3, 1) dot (1, 2, 2, 4) = (1 + 6 + 6 + 4).

Mathematica

LinearRecurrence[{5, -8, 4}, {1, 3, 7, 17}, 40] (* Harvey P. Dale, Apr 30 2022 *)

Prog

(PARI) Vec(x*(1-2*x+2*x^3)/((1-x)*(1-2*x)^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Crossrefs

Cf. A131055, A131054, A141222.

Sequence in context: A138901 A192674 A272480 * A077851 A089737 A123335

Adjacent sequences: A131053 A131054 A131055 * A131057 A131058 A131059

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 12 2007

Extensions

More terms from Paul Barry, Jun 14 2008

Status

approved