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A167784
a(n) = 2^n - (1 - (-1)^n)*3^((n-1)/2).
3
1, 0, 4, 2, 16, 14, 64, 74, 256, 350, 1024, 1562, 4096, 6734, 16384, 28394, 65536, 117950, 262144, 484922, 1048576, 1979054, 4194304, 8034314, 16777216, 32491550, 67108864, 131029082, 268435456, 527304974, 1073741824, 2118785834, 4294967296, 8503841150
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OFFSET
0,3
COMMENTS
Binomial transform of A077917, the signed variant of A127864.
LINKS
Robert Israel, Table of n, a(n) for n = 0..3318
Index entries for linear recurrences with constant coefficients, signature (2,3,-6).
FORMULA
a(n) = A167936(n+1) - A167936(n).
a(2n) = A000302(n). a(2n+1) = 2*A005061(n).
a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3).
G.f.: (x-1)^2/((2*x-1)*(3*x^2-1)).
a(n+4) mod 9 = A153130(n+4) = A146501(n+2), n>=0.
E.g.f.: exp(2*x) - (2/sqrt(3))*sinh(sqrt(3)*x). - G. C. Greubel, Jun 27 2016
MAPLE
seq(2^n - (1 - (-1)^n)*3^((n-1)/2), n=0..100); # Robert Israel, Apr 11 2019
MATHEMATICA
LinearRecurrence[{2, 3, -6}, {1, 0, 4}, 40] (* Harvey P. Dale, Nov 29 2011 *)
CROSSREFS
Cf. A154383.
Sequence in context: A154383 A022664 A316463 * A053125 A038232 A254632
Adjacent sequences: A167781 A167782 A167783 * A167785 A167786 A167787
KEYWORD
nonn,easy,changed
AUTHOR
Paul Curtz, Nov 12 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Feb 27 2010
Incorrect b-file corrected by Robert Israel, Apr 11 2019
STATUS
approved

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Last modified September 28 16:16 EDT 2024. Contains 376297 sequences.
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