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 (5, -4).
FORMULA
a(n) = 1 + Sum_{k=0..n} binomial(2*n-1, 2*k-1), for n > 0. - Paul Barry, May 26 2008
a(n) = A052539(n-1), n > 0. - R. J. Mathar, Jun 18 2008
From Sergei N. Gladkovskii, Dec 20 2011: (Start)
G.f.: (1 - 3*x - x^2)/((1-x)*(1-4*x)).
E.g.f.: (exp(4*x) + 4*exp(x) - 1)/4 = (G(0) - 1)/4; G(k) = 1 + 4/(4^k-x*16^k/(x*4^k+(k+1)/G(k+1))); (continued fraction). (End)
MAPLE
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=4*a[n-1] od: seq(a[n]+sum((k), k=0..1), n=0..20); # Zerinvary Lajos, Mar 20 2008
MATHEMATICA
A123162[n_, k_]= If [k==0, 1, Binomial[2*n-1, 2*k-1]];
Table[Sum[A123162[n, k], {k, 0, n}], {n, 0, 30}]
Table[4^(n-1) +1 -Boole[n==0]/4, {n, 0, 40}] (* G. C. Greubel, May 31 2022 *)
PROG
(Magma) [0] cat [4^(n-1) +1: n in [1..40]]; // G. C. Greubel, May 31 2022
(SageMath) [4^(n-1) +1 -bool(n==0)/4 for n in (0..40)] # G. C. Greubel, May 31 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Oct 02 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 04 2006
STATUS
approved