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A167910 a(n) = (4*3^n - 5*2^n + (-2)^n)/20. 1
0, 0, 1, 3, 13, 39, 133, 399, 1261, 3783, 11605, 34815, 105469, 316407, 953317, 2859951, 8596237, 25788711, 77431669, 232295007, 697147165, 2091441495, 6275373061, 18826119183, 56482551853, 169447655559, 508359743893, 1525079231679, 4575304803901, 13725914411703 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n+1) - 3a(n) = 0,1,0,4,0,16,0,64,.. is an "aerated" version of A000302.
LINKS
FORMULA
a(2*n+1) = 3*a(2*n).
a(n) = 3*a(n-1) + 4*a(n-2) - 12*a(n-3).
G.f.: x^2/((1-3*x)*(1-2*x)*(1+2*x)). - Philippe Deléham, Nov 15 2009
MATHEMATICA
LinearRecurrence[{3, 4, -12}, {0, 0, 1}, 40] (* Harvey P. Dale, Mar 29 2015 *)
PROG
(Magma) [(4*3^n-5*2^n+(-2)^n)/20: n in [0..40] ]; // Vincenzo Librandi, Aug 06 2011
CROSSREFS
Sequence in context: A122504 A103277 A166897 * A147042 A018492 A227446
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 15 2009
EXTENSIONS
Replaced definition by Lava formula of Nov 26 2009. Removed comments about unrelated sequences. - R. J. Mathar, Feb 27 2010
STATUS
approved

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Last modified June 19 23:45 EDT 2024. Contains 373510 sequences. (Running on oeis4.)