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A167122
a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 2; a(0) = 1, a(1) = 22, a(2) = 378.
5
1, 22, 378, 6155, 98911, 1584303, 25355759, 405719791, 6491627247, 103866478319, 1661865422575, 26589853839087, 425437689736943, 6807003149037295, 108912050837581551, 1742592815213244143, 27881485050659663599
OFFSET
0,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 16.
FORMULA
a(n) = (1451*16^n - 540*4^n + 64)/960, for n > 0.
G.f.: (1 + x + x^3)/((1-x)*(1-4*x)*(1-16*x)).
E.g.f.: (1/960)*(-15 + 64*exp(x) - 540*exp(4*x) + 1451*exp(16*x)). - G. C. Greubel, Jun 04 2016
MATHEMATICA
CoefficientList[Series[(1 + x + x^3)/((1-x)*(1-4*x)*(1-16*x)), {x, 0, 10}], x] (* G. C. Greubel, Jun 04 2016 *)
LinearRecurrence[{21, -84, 64}, {1, 22, 378, 6155}, 20] (* Harvey P. Dale, Sep 26 2023 *)
PROG
(Magma) [ n le 2 select 21*n-20 else n eq 3 select 378 else 20*Self(n-1)-64*Self(n-2)+3: n in [1..17] ];
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Oct 27 2009
STATUS
approved