A146884 a(n) = 7*Sum_{k=0..n} 6^k.
7, 49, 301, 1813, 10885, 65317, 391909, 2351461, 14108773, 84652645, 507915877, 3047495269, 18284971621, 109709829733, 658258978405, 3949553870437, 23697323222629, 142183939335781, 853103636014693, 5118621816088165
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-6).
Programs
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Magma
[n le 2 select 7^n else 7*Self(n-1) -6*Self(n-2): n in [1..31]]; // G. C. Greubel, Oct 12 2022
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Mathematica
a[n_]:= Sum[7*6^m, {m,0,n}]; Table[a[n], {n,0,30}] Accumulate[7*6^Range[0,20]] (* Harvey P. Dale, Dec 18 2021 *) -
SageMath
[(7/5)*(6^(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) = (7/5)*(6^(n+1) - 1).
a(n) = 7*A003464(n+1).
a(n) = 7*a(n-1) - 6*a(n-2).
G.f.: 7/((1-x)*(1-6*x)).
E.g.f.: (7/5)*(6*exp(6*x) - exp(x)). (End)