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URL: https://oeis.org/A135360

⇱ A135360 - OEIS

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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
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
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: A377252 A072641 A280352 * A347017 A082548 A270995
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 08 2007
EXTENSIONS
More terms from Michel Marcus, May 06 2015
STATUS
approved