OFFSET
0,2
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, 4, 0, 4, 0, 4, ...].
a(n) = 2^(n+1) - 3*n + 1, for n > 0. - R. J. Mathar, Apr 04 2012
From G. C. Greubel, Feb 14 2021: (Start)
G.f.: (1 - 2*x + 4*x^3)/((1-x)^2 * (1-2*x)).
E.g.f.: -2 + (1-3*x)*exp(x) + 2*exp(2*x). (End)
EXAMPLE
a(4) = 21 = sum of row 4 terms of triangle A132729: (1 + 5 + 9 + 5 + 1).
a(3) = 8 = (1, 3, 3, 1) dot (1, 1, 0, 4) = (1 + 3 + 0 + 4).
MATHEMATICA
LinearRecurrence[{4, -5, 2}, {1, 2, 3, 8}, 30] (* Harvey P. Dale, Dec 30 2015 *)
Table[2^(n+1) -3*n +1 -2*Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Feb 14 2021 *)
PROG
(Sage) [1]+[2^(n+1) -3*n +1 for n in (1..30)] # G. C. Greubel, Feb 14 2021
(Magma) [1] cat [2^(n+1) -3*n +1: n in [0..30]]; // G. C. Greubel, Feb 14 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 26 2007
STATUS
approved