A077943 Expansion of 1/(1 - 2*x + 2*x^2 - 2*x^3).
1, 2, 2, 2, 4, 8, 12, 16, 24, 40, 64, 96, 144, 224, 352, 544, 832, 1280, 1984, 3072, 4736, 7296, 11264, 17408, 26880, 41472, 64000, 98816, 152576, 235520, 363520, 561152, 866304, 1337344, 2064384, 3186688, 4919296, 7593984, 11722752, 18096128, 27934720, 43122688
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..5303
- Yassine Otmani, The 2-Pascal Triangle and a Related Riordan Array, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 17.
- Index entries for linear recurrences with constant coefficients, signature (2,-2,2).
Programs
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Mathematica
CoefficientList[Series[1/(1 - 2 x + 2 x^2 - 2 x^3), {x, 0, 50}], x] (* Harvey P. Dale, Nov 30 2011 *) LinearRecurrence[{2, -2, 2}, {1, 2, 2}, 50] (* Harvey P. Dale, Nov 30 2011 *) Table[RootSum[-2 + 2 # - 2 #^2 + #^3 &, 4 #^n - 6 #^(n + 1) + 7 #^(n + 2) &]/22, {n, 0, 20}] (* Eric W. Weisstein, Dec 14 2023 *) -
PARI
Vec(1/(1-2*x+2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
Formula
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3); a(0)=1, a(1)=2, a(2)=2. - Harvey P. Dale, Nov 30 2011
From R. J. Mathar, Mar 13 2021: (Start)
a(n) + a(n+1) = |A078071(n+1)|.
a(n) = (-1)^n*A077993(n). (End)
Comments