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

Author

Roger L. Bagula, May 27 2005

Keywords

• nonn
• easy
• less

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).

Crossrefs

Cf. A013984.

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

Programs

Magma

m:=40; R:=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

Mathematica

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

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

Formula

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

Extensions

Entry rewritten by Charles R Greathouse IV, Jan 26 2011