OFFSET
0,2
COMMENTS
Apart from initial terms, and with a change of offset, same as A095768. - Jon E. Schoenfield, Jun 15 2017
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
Binomial transform of (1, 1, 0, 2, 0, 2, 0, 2, 0, 2, ...).
For n>=1, a(n) = 2^n - n + 1 = A000325(n) + 1. - Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 17 2009. (Corrected by Franklin T. Adams-Watters, Jan 17 2009)
E.g.f.: U(0)- 1, where U(k) = 1 - x/(2^k + 2^k/(x - 1 - x^2*2^(k+1)/(x*2^(k+1) + (k+1)/U(k+1) ))). - Sergei N. Gladkovskii, Dec 01 2012
From Colin Barker, Mar 14 2014: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.
G.f.: (1-2*x+2*x^3) / ((1-x)^2*(1-2*x)). (End)
EXAMPLE
a(4) = 13 = sum of row 4 terms of triangle A132044: (1 + 3 + 5 + 3 + 1).
a(4) = 13 = (1, 4, 6, 4, 1) dot (1, 1, 0, 2, 0) = (1 + 4 + 0 + 8 + 0).
MATHEMATICA
Table[2^n -(n-1) -Boole[n==0], {n, 0, 35}] (* G. C. Greubel, Feb 12 2021 *)
PROG
(PARI) Vec((1-2*x+2*x^3)/((1-x)^2*(1-2*x)) + O(x^100)) \\ Colin Barker, Mar 14 2014
(Sage) [1]+[2^n -n +1 for n in (1..35)] # G. C. Greubel, Feb 12 2021
(Magma) [1] cat [2^n -n +1: n in [1..35]]; // G. C. Greubel, Feb 12 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 08 2007
STATUS
approved