A156158 a(n) = 6*a(n-1) - a(n-2) for n > 2; a(1) = 25, a(2) = 137.

25, 137, 797, 4645, 27073, 157793, 919685, 5360317, 31242217, 182092985, 1061315693, 6185801173, 36053491345, 210135146897, 1224757390037, 7138409193325, 41605697769913, 242495777426153, 1413368966787005

Offset: 1

Author

Klaus Brockhaus, Feb 09 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-1).

Crossrefs

Third trisection of A155923.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156157.

Programs

Mathematica

LinearRecurrence[{6,-1},{25,137},30] (* Harvey P. Dale, Jan 02 2019 *)

PARI

{m=19; v=concat([25,137], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

Formula

a(n) = ((26+7*sqrt(2))*(3-2*sqrt(2))^n+(26-7*sqrt(2))*(3+2*sqrt(2))^n)/4.

G.f.: x*(25-13*x)/(1-6*x+x^2).

Limit_{n -> oo} a(n)/a(n-1) = 3+2*sqrt(2).