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 A083579 Generalized Jacobsthal numbers. 6
 0, 1, 1, 4, 8, 19, 39, 82, 166, 337, 677, 1360, 2724, 5455, 10915, 21838, 43682, 87373, 174753, 349516, 699040, 1398091, 2796191, 5592394, 11184798, 22369609, 44739229, 89478472, 178956956, 357913927, 715827867, 1431655750, 2863311514 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2). FORMULA a(n) = (2^(n+3) - 5*(-1)^n - 3*(2*n+1))/12. a(n+2) = a(n+1) + 2*a(n) + n, a(0)=0, a(1)=1. G.f.: x*(1 - 2*x + 2*x^2)/(1 - 3*x + x^2 + 3*x^3 - 2*x^4). - Colin Barker, Jan 16 2012 MATHEMATICA LinearRecurrence[{3, -1, -3, 2}, {0, 1, 1, 4}, 40] (* G. C. Greubel, May 25 2019 *) PROG (PARI) concat(0, Vec(x*(1-2*x+2*x^2)/(1-3*x+x^2+3*x^3-2*x^4) + O(x^40))) \\ G. C. Greubel, May 25 2019 (MAGMA) I:=[0, 1, 1, 4]; [n le 4 select I[n] else 3*Self(n-1)-Self(n-2) - 3*Self(n-3)+2*Self(n-4): n in [1..40]]; // G. C. Greubel, May 25 2019 (Sage) (x*(1-2*x+2*x^2)/(1-3*x+x^2+3*x^3-2*x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019 (GAP) a:=[0, 1, 1, 4];; for n in [5..40] do a[n]:=3*a[n-1]-a[n-2]-3*a[n-3] +2*a[n-4]; od; a; # G. C. Greubel, May 24 2019 CROSSREFS Cf. A083580. Sequence in context: A163318 A129362 A301981 * A335714 A215112 A265108 Adjacent sequences:  A083576 A083577 A083578 * A083580 A083581 A083582 KEYWORD nonn,easy AUTHOR Paul Barry, May 01 2003 STATUS approved

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Last modified December 5 12:51 EST 2020. Contains 338947 sequences. (Running on oeis4.)