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 A122112 a(n) = 4*a(n-2) - a(n-1), with a(0)=1, a(1)=-2. 1
 1, -2, 6, -14, 38, -94, 246, -622, 1606, -4094, 10518, -26894, 68966, -176542, 452406, -1158574, 2968198, -7602494, 19475286, -49885262, 127786406, -327327454, 838473078, -2147782894, 5501675206, -14092806782, 36099507606, -92470734734 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-1,4). FORMULA a(n) = (-1)^n * A026597(n). a(n) = Sum_{k=0..n} (-2)^(n-k) * A055830(n,k). G.f.: (1-x)/(1+x-4*x^2). a(n) = (1/2) * (-1/2 - (1/2)*sqrt(17))^n + (3/34) * (-1/2 - (1/2)*sqrt(17))^n * sqrt(17) - (3/34)*sqrt(17) * (-1/2 + (1/2)*sqrt(17))^n + (1/2) * (-1/2 + (1/2)*sqrt(17))^n, with n >= 0. - Paolo P. Lava, Nov 19 2008 a(n) = (-2*i)^n*( ChebyshevU(n, -i/4) - (i/2)*ChebyshevU(n-1, -i/4) ). - G. C. Greubel, Dec 23 2021 E.g.f.: exp(-x/2)*(17*cosh(sqrt(17)*x/2) - 3*sqrt(17)*sinh(sqrt(17)*x/2))/17. - Stefano Spezia, Apr 03 2023 MAPLE seq(coeff(series((1-x)/(1+x-4*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 02 2019 MATHEMATICA LinearRecurrence[{-1, 4}, {1, -2}, 30] (* G. C. Greubel, Oct 02 2019 *) PROG (PARI) my(x='x+O('x^30)); Vec((1-x)/(1+x-4*x^2)) \\ G. C. Greubel, Oct 02 2019 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)/(1+x-4*x^2) )); // G. C. Greubel, Oct 02 2019 (Sage) def A122112_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1-x)/(1+x-4*x^2)).list() A122112_list(30) # G. C. Greubel, Oct 02 2019 (GAP) a:=[1, -2];; for n in [3..30] do a[n]:=-a[n-1]+4*a[n-2]; od; a; # G. C. Greubel, Oct 02 2019 CROSSREFS Cf. A026597, A055830. Sequence in context: A263758 A100067 A026597 * A190788 A168259 A275208 Adjacent sequences: A122109 A122110 A122111 * A122113 A122114 A122115 KEYWORD sign,easy AUTHOR Philippe Deléham, Oct 18 2006 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 STATUS approved

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Last modified October 3 17:45 EDT 2023. Contains 365870 sequences. (Running on oeis4.)