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%I A077880 #23 Aug 14 2024 23:14:04
%S A077880 1,1,3,2,6,2,11,-1,21,-12,44,-44,101,-131,247,-362,626,-970,1615,
%T A077880 -2565,4201,-6744,10968,-17688,28681,-46343,75051,-121366,196446,
%U A077880 -317782,514259,-832009,1346301,-2178276,3524612,-5702852,9227501,-14930315,24157855,-39088130,63246026,-102334114
%N A077880 Expansion of (1-x)^(-1)/(1-2*x^2+x^3).
%H A077880 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -3, 1).
%F A077880 a(n) = (-1)^n*Fibonacci(n-1) + n. - _Vladeta Jovovic_, Jul 18 2004
%F A077880 a(n) = A001924(-3-n) = 2*a(n-2) - a(n-3) + 1. - _Michael Somos_, Dec 31 2012
%F A077880 If 0 is prepended then BINOMIAL transform is A079282 with 0 prepended. - _Michael Somos_, Dec 31 2012
%F A077880 a(n) = (-1)^n * Sum_{k=0..n} binomial(k-2,n-k). - _Seiichi Manyama_, Aug 14 2024
%e A077880 1 + x + 3*x^2 + 2*x^3 + 6*x^4 + 2*x^5 + 11*x^6 - x^7 + 21*x^8 - 12*x^9 + 44*x^10 + ...
%t A077880 Table[(-1)^n*Fibonacci[n - 1] + n, {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 28 2011 *)
%o A077880 (PARI) {a(n) = fibonacci(1-n) + n} /* _Michael Somos_, Dec 31 2012 */
%Y A077880 Cf. A000045.
%K A077880 sign
%O A077880 0,3
%A A077880 _N. J. A. Sloane_, Nov 17 2002

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