A127985 a(n) = floor(2^n*(n/3 + 4/9)).
0, 1, 4, 11, 28, 67, 156, 355, 796, 1763, 3868, 8419, 18204, 39139, 83740, 178403, 378652, 800995, 1689372, 3553507, 7456540, 15612131, 32622364, 68040931, 141674268, 294533347, 611436316, 1267611875, 2624702236, 5428361443
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Ray Chandler, Jan 19 2019)
- Wieb Bosma, Signed bits and fast exponentiation, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41.
- Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,4).
Crossrefs
Programs
-
Magma
[(n/3 + 4/9)*2^n - 1/2 + (-1)^n/18: n in [1..40]]; // Vincenzo Librandi, May 26 2011
-
Mathematica
Table[(n/3 + 4/9) 2^n - 1/2 + (-1)^n/18, {n, 1, 50}] LinearRecurrence[{4,-3,-4,4},{1,4,11,28},50] (* Harvey P. Dale, May 15 2011 *) -
PARI
a(n)=(n*3+4)<
Formula
a(n) = (n/3 + 4/9)*2^n - 1/2 + (-1)^n/18.
a(1)=1, a(2)=4, a(3)=11, a(4)=28, a(n) = 4*a(n-1)-3*a(n-2)-4*a(n-3)+4*a(n-4). - Harvey P. Dale, May 15 2011
G.f.: x*(1-2*x^2)/((1-2*x)^2*(1-x^2)). - Harvey P. Dale, May 15 2011
E.g.f.: ((4 + 6*x)*cosh(2*x) - 5*sinh(x) + 4*cosh(x)*((2 + 3*x)*sinh(x) - 1))/9. - Stefano Spezia, May 25 2023
Extensions
Definition simplified by M. F. Hasler, Oct 07 2014
Sequence extended to a(0)=0 by M. F. Hasler, Oct 08 2014