A152596 a(n) = 7*a(n-1) - 6*a(n-2), n>1; a(0)=1, a(1)=3.

1, 3, 15, 87, 519, 3111, 18663, 111975, 671847, 4031079, 24186471, 145118823, 870712935, 5224277607, 31345665639, 188073993831, 1128443962983, 6770663777895, 40623982667367, 243743896004199, 1462463376025191, 8774780256151143, 52648681536906855, 315892089221441127

Offset: 0

Author

Philippe Deléham, Dec 09 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-6).

Crossrefs

Cf. A147703.

Programs

Mathematica

Table[MatrixPower[{{3,2},{3,4}},n][[1]][[1]],{n,0,44}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{7,-6},{1,3},30] (* Harvey P. Dale, Jul 27 2021 *)

Formula

G.f.: (1-4*x)/(1 - 7*x + 6*x^2).

a(n) = Sum_{k=0..n} A147703(n,k)*2^(n-k).

a(n) = (1/5)*(3 + 2*6^n), with n>=0. - Paolo P. Lava, Dec 12 2008

E.g.f.: exp(x)*(3 + 2*exp(5*x))/5. - Stefano Spezia, Sep 30 2023

Extensions

a(21)-a(23) from Stefano Spezia, Sep 30 2023