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
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 12 2007
EXTENSIONS
More terms from Paul Barry, Jun 14 2008
STATUS
approved