A256959 a(0)=1, a(1)=4; thereafter a(n) = 13*4^n/8-2^(n+1)+1.

1, 4, 19, 89, 385, 1601, 6529, 26369, 105985, 424961, 1701889, 6811649, 27254785, 109035521, 436174849, 1744764929, 6979190785, 27917025281, 111668625409, 446675550209, 1786704297985, 7146821386241, 28587293933569, 114349192511489, 457396803600385

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Paul K. Stockmeyer, The Pascal Rhombus and the Stealth Configuration, arXiv:1504.04404 [math.CO], 2015.

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3). - Colin Barker, Jun 05 2015

G.f.: (4*x^4-4*x^3-5*x^2+3*x-1) / ((x-1)*(2*x-1)*(4*x-1)). - Colin Barker, Jun 05 2015

a(n) = (2^n)^2 + (2^n-1)^2 - (2^(n-1))^2 - 2*(2^(n-2))^2 (see (4) in arXiv link). - Michel Marcus, Jun 06 2015

Mathematica

Join[{1, 4}, Table[13 4^n/8 - 2^(n + 1) + 1, {n, 2, 40}]] (* Vincenzo Librandi, Jun 06 2015 *)
LinearRecurrence[{7, -14, 8}, {1, 4, 19, 89, 385}, 30] (* Harvey P. Dale, Feb 20 2020 *)

Prog

(PARI) Vec((4*x^4-4*x^3-5*x^2+3*x-1) / ((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jun 05 2015
(Magma) I:=[1, 4, 19, 89, 385]; [n le 5 select I[n] else 7*Self(n-1)-14*Self(n-2)+8*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 06 2015

Crossrefs

Sequence in context: A192526 A084155 A015530 * A181880 A291016 A010907

Adjacent sequences: A256956 A256957 A256958 * A256960 A256961 A256962

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 14 2015

Status

approved