OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 12.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
FORMULA
a(n) = 2^(2+n)*n for n>0. - Colin Barker, Apr 23 2014
a(n) = 4*a(n-1)-4*a(n-2) for n>2. - Colin Barker, Apr 23 2014
From Amiram Eldar, Jan 13 2021: (Start)
Sum_{n>=1} 1/a(n) = log(2)/4.
Sum_{n>=1} (-1)^(n+1)/a(n) = log(3/2)/4. (End)
E.g.f.: 1 + 8*x*exp(x). - G. C. Greubel, Jun 07 2023
MAPLE
MATHEMATICA
Table[2^(n+2)*n + Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 07 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 41); Coefficients(R!((1+2*x)^2/(1-2*x)^2));
(PARI) Vec((2*x+1)^2/(2*x-1)^2 + O(x^100)) \\ Colin Barker, Apr 22 2014
(Sage)
def A241204(i):
if i==0: return 1
else: return 2^(2+i)*i;
[A241204(n) for n in (0..30)] # Bruno Berselli, Apr 23 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Lopatin and Juri-Stepan Gerasimov, Apr 17 2014
STATUS
approved