A146885 a(n) = 8*Sum_{k=0..n} 7^k.
8, 64, 456, 3200, 22408, 156864, 1098056, 7686400, 53804808, 376633664, 2636435656, 18455049600, 129185347208, 904297430464, 6330082013256, 44310574092800, 310174018649608, 2171218130547264, 15198526913830856
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (8,-7).
Programs
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Magma
[n le 2 select 8^n else 8*Self(n-1) -7*Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 12 2022
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Mathematica
a[n_]:= Sum[8*7^m, {m,0,n}]; Table[a[n], {n,0,30}] LinearRecurrence[{8,-7}, {8,64}, 41] (* G. C. Greubel, Oct 12 2022 *) -
SageMath
[(4/3)*(7^(n+1)-1) for n in range(41)] # G. C. Greubel, Oct 12 2022
Formula
From G. C. Greubel, Oct 12 2022: (Start)
a(n) = (4/3)*(7^(n+1) - 1).
a(n) = 8*A023000(n+1).
a(n) = 8*a(n-1) - 7*a(n-2).
G.f.: 8/((1-x)*(1-7*x)).
E.g.f.: (4/3)*(7*exp(7*x) - exp(x)). (End)