A190972 a(n) = 7*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.

0, 1, 7, 46, 301, 1969, 12880, 84253, 551131, 3605158, 23582713, 154263517, 1009096480, 6600884809, 43178904223, 282449675134, 1847611013269, 12085928067481, 79058663432560, 517152859825477, 3382894028480659, 22128799619888182, 144752915253775297

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn
• easy

Comments

a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6} avoiding 01, 02 and 03. - Milan Janjic, Dec 17 2015

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-3).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else 7*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015

Mathematica

LinearRecurrence[{7,-3}, {0,1}, 50]

PARI

concat(0, Vec(x/(1-7*x+3*x^2) + O(x^100))) \\ Altug Alkan, Dec 18 2015

Formula

a(n) = ((7/2 + 1/2*sqrt(37))^n - (7/2 - 1/2*sqrt(37))^n)/sqrt(37). - Giorgio Balzarotti, May 28 2011

G.f.: x/(1 - 7x + 3*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (2/sqrt(37))*exp(7*x/2)*sinh(sqrt(37)*x/2). - G. C. Greubel, Dec 18 2015