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A142974
A007318 * [1, 1, -1, 1, 1, 1, ...].
3
1, 2, 2, 2, 4, 12, 34, 86, 200, 440, 934, 1938, 3964, 8036, 16202, 32558, 65296, 130800, 261838, 523946, 1048196, 2096732, 4193842, 8388102, 16776664, 33553832, 67108214, 134217026, 268434700, 536870100, 1073740954, 2147482718
OFFSET
1,2
FORMULA
Binomial transform of [1, 1, -1, 1, 1, 1, ...].
From R. J. Mathar, Jul 31 2008: (Start)
O.g.f.: x(1-3x+x^2+3x^3)/((1-x)^3*(1-2x)).
a(n) = 4n - 2 - 2*A000217(n) + 2^(n-1). (End)
a(n) = 2^n - n(n-1) (if offset is 0). - Emeric Deutsch, Aug 09 2008
EXAMPLE
a(6) = 12 = (1, 5, 10, 10, 5, 1) dot (1, 1, -1, 1, 1, 1) = (1 + 5 - 10 + 10, + 5, + 1).
MAPLE
a:=proc(n) options operator, arrow: 2^n-n*(n-1) end proc: seq(a(n), n=0..32); # Emeric Deutsch, Aug 09 2008
MATHEMATICA
Table[2^n-n(n-1), {n, 0, 3*4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2010 *)
CROSSREFS
Sequence in context: A374663 A067920 A107902 * A259856 A375520 A279805
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 15 2008
EXTENSIONS
More terms from Emeric Deutsch, Aug 09 2008
STATUS
approved