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 A120748 Expansion of x^2*(1 + 2*x - x^2)/(1 - x - 3*x^2 - x^3 + x^4). 1
 0, 1, 3, 5, 15, 32, 79, 185, 439, 1041, 2464, 5841, 13835, 32781, 77663, 184000, 435935, 1032817, 2446959, 5797345, 13735104, 32541281, 77096979, 182658581, 432755695, 1025287136, 2429115823, 5755074345, 13634953255, 32304004977, 76534823264, 181326717105 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Lim_{n->oo} a(n)/a(n-1) is 2.3692054...; largest real eigenvalue of M and a root of the characteristic polynomial x^4 - x^3 - 3x^2 - x + 1. a(n) is the top left entry of the n-th power of the 4 X 4 matrix M = [0,1,1,0; 1,1,1,0; 0,1,0,1; 1,0,1,0]. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,1,-1). FORMULA a(n) = a(n-1) + 3*a(n-2) + a(n-3) - a(n-4). EXAMPLE a(8) = 439 = a(7) + 3*a(6) + a(5) - a(4) = 185 + 3*79 + 32 - 15. MATHEMATICA LinearRecurrence[{1, 3, 1, -1}, {0, 1, 3, 5}, 40] (* Amiram Eldar, Feb 28 2020 *) PROG (Magma) I:=[0, 1, 3, 5]; [n le 4 select I[n] else Self(n-1) +3*Self(n-2) +Self(n-3) -Self(n-4): n in [1..41]]; // G. C. Greubel, Nov 13 2022 (SageMath) def A120748_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( x^2*(1+2*x-x^2)/(1-x-3*x^2-x^3+x^4) ).list() a=A120748_list(40); a[1:] # G. C. Greubel, Nov 13 2022 CROSSREFS Sequence in context: A127978 A018470 A281438 * A182143 A193649 A186341 Adjacent sequences: A120745 A120746 A120747 * A120749 A120750 A120751 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Jul 01 2006 EXTENSIONS More terms from Amiram Eldar, Feb 28 2020 STATUS approved

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)