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A156158
a(n) = 6*a(n-1) - a(n-2) for n > 2; a(1) = 25, a(2) = 137.
4
25, 137, 797, 4645, 27073, 157793, 919685, 5360317, 31242217, 182092985, 1061315693, 6185801173, 36053491345, 210135146897, 1224757390037, 7138409193325, 41605697769913, 242495777426153, 1413368966787005
OFFSET
1,1
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).
MATHEMATICA
LinearRecurrence[{6, -1}, {25, 137}, 30] (* Harvey P. Dale, Jan 02 2019 *)
PROG
(PARI) {m=19; v=concat([25, 137], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
CROSSREFS
Third trisection of A155923.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156157.
Sequence in context: A364194 A317217 A147489 * A195977 A233368 A240415
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Feb 09 2009
STATUS
approved