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A167193 a(n) = (1/3)*(1 - (-2)^n + 3*(-1)^n ) = (-1)^(n+1)*A167030(n). 1
1, 0, 0, 2, -4, 10, -20, 42, -84, 170, -340, 682, -1364, 2730, -5460, 10922, -21844, 43690, -87380, 174762, -349524, 699050, -1398100, 2796202, -5592404, 11184810, -22369620, 44739242, -89478484, 178956970, -357913940, 715827882, -1431655764, 2863311530, -5726623060, 11453246122, -22906492244, 45812984490 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
This is the inverse binomial transform of 1, 1, 1, 3, 5, 11,.. (continued as in A001045 and conjectured to be equal to A152046).
Any sequence (like this one) which obeys a(n)= -2a(n-1)+a(n-2)+2a(n-3) also obeys a(n)=5a(n-2)-4a(n-4), proved by telescoping; see A101622.
LINKS
FORMULA
a(2n) = (-1)^n* A084240(n). a(2n+1) = A020988(n).
G.f.: ( -1 - 2*x + x^2 ) / ( (x-1)*(1+2*x)*(1+x) ).
a(n) = -a(n-1) + 2*a(n-2) - 2*(-1)^n.
a(n) = -2*a(n-1) + a(n-2) + 2*a(n-3).
E.g.f.: (1/3)*(exp(x) + 3*exp(-x) - exp(-2*x)). - G. C. Greubel, Jun 04 2016
MATHEMATICA
LinearRecurrence[{-2, 1, 2}, {1, 0, 0}, 25] (* or *) Table[(1/3)*(1 + 3*(-1)^n - (-2)^n), {n, 0, 25}] (* G. C. Greubel, Jun 04 2016 *)
PROG
(Magma) [( 1-(-1)^n*2^n)/3+(-1)^n: n in [0..40] ]; // Vincenzo Librandi, Aug 06 2011
CROSSREFS
Sequence in context: A255386 A167030 A026644 * A026666 A325508 A238439
KEYWORD
easy,sign
AUTHOR
Paul Curtz, Oct 30 2009
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)