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A083885
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(4^n+2^n+0^n+(-2)^n)/4
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2
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1, 1, 6, 16, 72, 256, 1056, 4096, 16512, 65536, 262656, 1048576, 4196352, 16777216, 67117056, 268435456, 1073774592, 4294967296, 17180000256, 68719476736, 274878431232, 1099511627776, 4398048608256, 17592186044416, 70368752566272
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A083884.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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a(n) = (4^n+2^n+0^n+(-2)^n)/4.
G.f.: (4*x^3-2*x^2-3*x+1)/((2*x+1)*(2*x-1)*(4*x-1)).
E.g.f.: exp(4*x)+exp(2*x)+exp(0)+exp(-2*x).
A007814(a(n)) = A022998(n-1). - R. Stephan, Feb 14 2004
a(0)=1, a(1)=1, a(2)=6, a(3)=16, a(n)=4*a(n-1)+4*a(n-2)-16*a(n-3) [From Harvey P. Dale, Dec 12 2011]
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MATHEMATICA
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Join[{1}, Table[(4^n+2^n+(-2)^n)/4, {n, 30}]] (* or *) Join[{1}, LinearRecurrence[ {4, 4, -16}, {1, 6, 16}, 30]] (* From Harvey P. Dale, Dec 12 2011 *)
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PROG
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(MAGMA) [(4^n+2^n+0^n+(-2)^n)/4: n in [0..20]]; // Vincenzo Librandi, Jun 16 2011
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CROSSREFS
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Sequence in context: A128243 A118640 A142704 * A211954 A188570 A009352
Adjacent sequences: A083882 A083883 A083884 * A083886 A083887 A083888
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, May 09 2003
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STATUS
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approved
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