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M. C. Firengiz, A. Dil, <a href="http://www.nntdm.net/papers/nntdm-20/NNTDM-20-4-21-32.pdf">Generalized Euler-Seidel method for second order recurrence relations</a>, Notes on Number Theory and Discrete Mathematics, Vol. 20, 2014, No. 4, 21-32.
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a(n) = ((-1-sqrt(2))^(n-1) + (-1+sqrt(2))^(n-1))/2 + sqrt(2)*((-1+sqrt(2))^(n-1) - (-1 -sqrt(2))^(n-1))/4, for n > 0. - Paolo P. Lava, Oct 26 2012
approved
(MAGMA) [1, 1] cat [n le 2 select (n-1) else -2*Self(n-1)+Self(n-2): n in [1..35] ]; // Vincenzo Librandi, Sep 09 2013
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a(n) = -2*a(n-1) + a(n-2) for n>2, with a(0) = a(1) = 1, a(2) = 0.
a(n) = Sum_{k, 0<=k<=n} A147746(n,k)*(-1)^(n-k) . - Philippe Deléham, Aug 30 2012
a(n) = ((-1-sqrt(2))^(n-1)+(-1+sqrt(2))^(n-1))/2 +sqrt(2)*((-1+sqrt(2))^(n-1)-(-1 -sqrt(2))^(n-1))/4, for n>0. [_Paolo P. Lava_, Oct 26 2012]
G.f.: 1+x + x^2/(1-x) - G(0)*x^2 /(2-2*x), where G(k)= 1 + 1/(1 - x*(2*k-1)/(x*(2*k+1) + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 10 2013
a(n) = (-1)^n a(1-n) = A000129(-1-n) if n<0. a(n-2) = 2*a(n-1) + a(n) if n<1 or n>2. - Michael Somos, Mar 19 2019
approved
editing