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 A083885 (4^n+2^n+0^n+(-2)^n)/4 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A083884. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA 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] MATHEMATICA 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 *) PROG (MAGMA) [(4^n+2^n+0^n+(-2)^n)/4: n in [0..20]]; // Vincenzo Librandi, Jun 16 2011 CROSSREFS Sequence in context: A128243 A118640 A142704 * A211954 A188570 A009352 Adjacent sequences:  A083882 A083883 A083884 * A083886 A083887 A083888 KEYWORD easy,nonn AUTHOR Paul Barry, May 09 2003 STATUS approved

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