A107480 a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-7).

0, 1, 1, 2, 3, 5, 8, 14, 25, 42, 71, 121, 207, 353, 601, 1025, 1748, 2980, 5080, 8661, 14767, 25176, 42922, 73178, 124762, 212707, 362644, 618273, 1054096, 1797131, 3063933, 5223708, 8905915, 15183719, 25886764, 44134416, 75244889, 128285220, 218713827

Offset

0,4

Comments

Lim_{n->infinity} a(n)/a(n-1) = 1.70490277..., the real root of x^5 = x^4 + x^3 + 1.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Peter Borwein and Kevin G. Hare, Some computations on Pisot and Salem numbers, 2000, table 1, p. 7.

Peter Borwein and Kevin G. Hare, Some computations on the spectra of Pisot and Salem numbers, Math. Comp. 71 (2002), 767-780.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,1,0,1).

Formula

G.f.: x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)). - Colin Barker, Dec 17 2017

Mathematica

LinearRecurrence[{1, 0, 1, 1, 1, 0, 1}, {0, 1, 1, 2, 3, 5, 8}, 50] (* Harvey P. Dale, May 21 2012 *)

Prog

(PARI) concat([0], Vec(x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)) + O(x^40))) \\ Colin Barker, Dec 17 2017
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1 +x^2-x^5)/((1+x^2)*(1-x-x^2-x^5)))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A013984.

Cf. A107479, A109538, A109543, A109544, A114749, A125950, A130844, A143335, A147851.

Sequence in context: A290075 A104882 A091956 * A345235 A128021 A036241

Adjacent sequences: A107477 A107478 A107479 * A107481 A107482 A107483

Keyword

nonn,easy,less

Author

Roger L. Bagula, May 27 2005

Extensions

Entry rewritten by Charles R Greathouse IV, Jan 26 2011

Status

approved