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A131885
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) for n >= 4 starting with a(0) = 1, a(1) = 2, a(2) = 4, and a(3) = 6.
1
1, 2, 4, 6, 8, 12, 24, 56, 128, 272, 544, 1056, 2048, 4032, 8064, 16256, 32768, 65792, 131584, 262656, 524288, 1047552, 2095104, 4192256, 8388608, 16781312, 33562624, 67117056, 134217728, 268419072, 536838144, 1073709056, 2147483648, 4295032832, 8590065664
OFFSET
0,2
LINKS
Karl Dilcher and Maciej Ulas, Divisibility and Arithmetic Properties of a Class of Sparse Polynomials, arXiv:2008.13475 [math.NT], 2020. See Table 1, 2nd column, p. 3.
FORMULA
Binomial transform of 1, 1, 1, -1.
G.f.: (-1 + 2*x - 2*x^2 + 2*x^3)/(2*x - 1)/(2*x^2 - 2*x + 1). - R. J. Mathar, Nov 14 2007
a(n) = 2*A038504(n) for n > 0. - R. J. Mathar, Jul 17 2009
G.f.: 1/2*(1 - 1/(2*x-1) + x*Q(0)/(1-x)), where Q(k) = 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/Q(k+1) )) (continued fraction). - Sergei N. Gladkovskii, Sep 27 2013
a(n) = Sum_{j=0..n} binomial(n, j)*(-1)^binomial(j, 3); this is the case m=3 and z=-1 of f(m,n)(z) = Sum_{j=0..n} binomial(n, j)*z^binomial(j, m). See Dilcher and Ulas. - Michel Marcus, Sep 01 2020
MATHEMATICA
Join[{1}, LinearRecurrence[{4, -6, 4}, {2, 4, 6}, 60]] (* Harvey P. Dale, Jul 07 2011 *)
CROSSREFS
Sequence in context: A374781 A340014 A001217 * A173941 A194406 A371164
KEYWORD
nonn
AUTHOR
Paul Curtz, Oct 25 2007
EXTENSIONS
More terms from Harvey P. Dale, Jul 07 2011
STATUS
approved