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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
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 (list; graph; refs; listen; history; text; internal format)
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 * A082548 A270995 A007323

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

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Last modified December 15 03:08 EST 2017. Contains 296020 sequences.