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

0,3

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).

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

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 *)

Prog

(Magma) [(n/3 + 4/9)*2^n - 1/2 + (-1)^n/18: n in [1..40]]; // Vincenzo Librandi, May 26 2011
(PARI) a(n)=(n*3+4)<<n\9 \\ M. F. Hasler, Oct 07 2014

Crossrefs

Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A127983, A127984, A073371, A000337.

Sequence in context: A370943 A003230 A099326 * A339252 A005409 A245124

Adjacent sequences: A127982 A127983 A127984 * A127986 A127987 A127988

Keyword

nonn,easy

Author

Artur Jasinski, Feb 09 2007

Extensions

Definition simplified by M. F. Hasler, Oct 07 2014

Sequence extended to a(0)=0 by M. F. Hasler, Oct 08 2014

Status

approved