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

Author

Paul Curtz, Dec 08 2007

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000079 (2^n), A000749.

Programs

Mathematica

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

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

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]

Extensions

More terms from Michel Marcus, May 06 2015