A218733 a(n) = (30^n - 1)/29.
0, 1, 31, 931, 27931, 837931, 25137931, 754137931, 22624137931, 678724137931, 20361724137931, 610851724137931, 18325551724137931, 549766551724137931, 16492996551724137931, 494789896551724137931, 14843696896551724137931, 445310906896551724137931, 13359327206896551724137931
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..600
- Index entries related to partial sums.
- Index entries for linear recurrences with constant coefficients, signature (31,-30).
Crossrefs
Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.
Cf. A009974.
Programs
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Magma
[n le 2 select n-1 else 31*Self(n-1) - 30*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
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Mathematica
LinearRecurrence[{31, -30}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *) (30^Range[0,20]-1)/29 (* Harvey P. Dale, Nov 22 2022 *) -
Maxima
A218733(n):=floor((30^n-1)/29)$ makelist(A218733(n),n,0,30); /* Martin Ettl, Nov 05 2012 */
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PARI
A218733(n)=30^n\29
Formula
a(n) = floor(30^n/29).
From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1-x)*(1-30*x)).
a(n) = 31*a(n-1) - 30*a(n-2). (End)
E.g.f.: exp(x)*(exp(29*x) - 1)/29. - Elmo R. Oliveira, Aug 29 2024
Comments