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URL: https://oeis.org/A166917

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A166917
a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 85, a(1) = 1364.
9
85, 1364, 21840, 349504, 5592320, 89478144, 1431654400, 22906486784, 366503854080, 5864061927424, 93824991887360, 1501199874392064, 24019198007050240, 384307168179912704, 6148914691147038720, 98382635059426361344, 1574122160955116748800, 25185954575299047849984
OFFSET
0,1
COMMENTS
Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+5) = 240*a(n).
FORMULA
a(n) = (256*16^n - 4^n)/3.
G.f.: (85 - 336*x)/((1-4*x)*(1-16*x)).
Limit_{n -> infinity} a(n)/a(n-1) = 16.
E.g.f.: (1/3)*(256*exp(16*x) - exp(4*x)). - G. C. Greubel, May 28 2016
MATHEMATICA
LinearRecurrence[{20, -64}, {85, 1364}, 50] (* G. C. Greubel, May 28 2016 *)
PROG
(PARI) {m=15; v=concat([85, 1364], vector(m-2)); for(n=3, m, v[n]=20*v[n-1]-64*v[n-2]); v}
(Magma)
[Binomial(4^(n+4), 2)/384: n in [0..30]]; // G. C. Greubel, Oct 02 2024
(SageMath)
A166917=BinaryRecurrenceSequence(20, -64, 85, 1364)
[A166917(n) for n in range(31)] # G. C. Greubel, Oct 02 2024
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Oct 27 2009
STATUS
approved