A133086 Row sums of triangle A133085.

1, 4, 10, 26, 64, 152, 352, 800, 1792, 3968, 8704, 18944, 40960, 88064, 188416, 401408, 851968, 1802240, 3801088, 7995392, 16777216, 35127296, 73400320, 153092096, 318767104, 662700032, 1375731712, 2852126720, 5905580032, 12213813248, 25232932864

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4).

Formula

Binomial transform of A114753: (1, 3, 3, 7, 5, 11, 7, 15, ...).

For n>1, a(n) = 2^n + 3*n*2^(n-2). - R. J. Mathar, Apr 04 2012

Example

a(3) = 26 = sum of row 3 of triangle A133085: (12 + 8, + 5 + 1).
a(3) = 26 = (1, 3, 3, 1) dot (1, 3, 3, 7) = (1 + 9 + 9 + 7).

Mathematica

Join[{1, 4}, Table[2^n + 3*n*2^(n - 2), {n, 2, 50}]] (* G. C. Greubel, Oct 21 2017 *)
LinearRecurrence[{4, -4}, {1, 4, 10, 26}, 40] (* Harvey P. Dale, Jul 19 2020 *)

Prog

(PARI) concat([1, 4], for(n=2, 50, print1(2^n + 3*n*2^(n-2), ", "))) \\ G. C. Greubel, Oct 21 2017
(Magma) [1, 4] cat [2^n+3*n*2^(n-2): n in [2..30]]; // Vincenzo Librandi, Oct 21 2017

Crossrefs

Cf. A133085, A114753, A133080.

Sequence in context: A000293 A000294 A308723 * A285186 A178037 A175658

Adjacent sequences: A133083 A133084 A133085 * A133087 A133088 A133089

Keyword

nonn

Author

Gary W. Adamson, Sep 08 2007

Status

approved