A135360 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) for n > 4, with first terms 1, 2, 4, 7.

1, 2, 4, 7, 12, 22, 44, 92, 192, 392, 784, 1552, 3072, 6112, 12224, 24512, 49152, 98432, 196864, 393472, 786432, 1572352, 3144704, 6290432, 12582912, 25167872, 50335744, 100667392, 201326592, 402644992, 805289984, 1610596352, 3221225472, 6442483712, 12884967424

Offset

0,2

Comments

Sequence identical to its fourth differences.

Without a(3)=7, sequence A000079 would have been obtained. - Michel Marcus, May 06 2015

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4).

Formula

a(n) = 2^n + A000749(n). - Michel Marcus, May 06 2015

G.f.: (1 - x)*(1 - x + x^2)/((1 - 2*x)*(1 - 2*x + 2*x^2)). [Bruno Berselli, May 06 2015]

Mathematica

Join[{1}, LinearRecurrence[{4, -6, 4}, {2, 4, 7}, 25]] (* G. C. Greubel, Oct 11 2016 *)

Prog

(PARI) lista(nn) = {v = vector(nn); v[1] = 1; v[2] = 2; v[3] = 4; v[4] = 7; for (k=5, nn, v[k] = 4*v[k-1]-6*v[k-2]+4*v[k-3]; ); v; } \\ Michel Marcus, May 06 2015

Crossrefs

Cf. A000079 (2^n), A000749.

Sequence in context: A023432 A072641 A280352 * A347017 A082548 A270995

Adjacent sequences: A135357 A135358 A135359 * A135361 A135362 A135363

Keyword

nonn,easy

Author

Paul Curtz, Dec 08 2007

Extensions

More terms from Michel Marcus, May 06 2015

Status

approved