OFFSET
0,2
COMMENTS
A transform of 4^n under the matrix A103452.
The square of the cotangent of the arcsin of 1/(2^n). - Al Hakanson (hawkuu(AT)excite.com), Feb 23 2006
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (5,-4).
FORMULA
G.f.: (1 - 2*x + 4*x^2)/((1-x)*(1-4*x));
a(n) = Sum_{k=0..n} A103452(n, k)*4^k;
a(n) = Sum_{k=0..n} (2*0^(n-k) - 1)*0^(k*(n-k))4^k.
a(n) = A024036(n), n > 0. - R. J. Mathar, Aug 30 2008
E.g.f.: 1 - exp(x) + exp(4*x). - G. C. Greubel, Jun 21 2021
a(n) = 5*a(n-1) - 4*a(n-2). - Wesley Ivan Hurt, Mar 17 2023
MATHEMATICA
Table[Boole[n==0] +4^n -1, {n, 0, 40}] (* G. C. Greubel, Jun 21 2021 *)
PROG
(Magma) [0^n+4^n-1: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011
(Sage) [1]+[4^n -1 for n in [1..40]] # G. C. Greubel, Jun 21 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 06 2005
STATUS
approved