A166917 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 85, a(1) = 1364.

85, 1364, 21840, 349504, 5592320, 89478144, 1431654400, 22906486784, 366503854080, 5864061927424, 93824991887360, 1501199874392064, 24019198007050240, 384307168179912704, 6148914691147038720, 98382635059426361344, 1574122160955116748800, 25185954575299047849984

Offset: 0

Author

Klaus Brockhaus, Oct 27 2009

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n+5) = 240*a(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (20, -64).

Crossrefs

Cf. A075153, A166912, A166913, A166914, A166915, A166916, A166927, A166965, A166984.

Programs

Magma

[Binomial(4^(n+4), 2)/384: n in [0..30]]; // G. C. Greubel, Oct 02 2024

Mathematica

LinearRecurrence[{20,-64}, {85, 1364}, 50] (* G. C. Greubel, May 28 2016 *)

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}

SageMath

A166917=BinaryRecurrenceSequence(20,-64,85,1364)
[A166917(n) for n in range(31)] # G. C. Greubel, Oct 02 2024

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