OFFSET
0,1
COMMENTS
Apart from a(0): Row sums of triangle A132752 (old name).
Apart from a(0): Binomial transform of [1, 3, 0, 4, 0, 4, 0, 4, ...].
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
From Colin Barker, Mar 14 2014: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
G.f.: (3 - 8*x + 6*x^2)/((1-x)^2 * (1-2*x)). (End)
E.g.f.: (1-x)*exp(x) + 2*exp(2*x). - G. C. Greubel, Feb 16 2021
EXAMPLE
a(3) = 14 = sum of row 3 terms of triangle A132752: (3 + 5 + 5 + 1).
a(3) = 14 = (1, 3, 3, 1) dot (1, 3, 0, 4) = (1 + 9 + 0 + 4).
MAPLE
MATHEMATICA
Table[2^(n+1) -n+1, {n, 0, 30}] (* Bruno Berselli, Aug 31 2013 *)
PROG
(PARI) a(n)=2^(n+1)-n+1
(PARI) Vec( (3-8*x+6*x^2)/((1-x)^2*(1-2*x)) + O(x^40)) \\ Colin Barker, Mar 14 2014
(Sage) [2^(n+1) -n+1 for n in (0..40)] # G. C. Greubel, Feb 16 2021
(Magma) [2^(n+1) -n+1: n in [0..40]]; // G. C. Greubel, Feb 16 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 28 2007
EXTENSIONS
More terms Vladimir Joseph Stephan Orlovsky, Dec 25 2008
Changed first member, and better name from Ralf Stephan, Aug 31 2013
STATUS
approved