A218739 a(n) = (36^n - 1)/35.
0, 1, 37, 1333, 47989, 1727605, 62193781, 2238976117, 80603140213, 2901713047669, 104461669716085, 3760620109779061, 135382323952046197, 4873763662273663093, 175455491841851871349, 6316397706306667368565, 227390317427040025268341, 8186051427373440909660277
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..600
- Index entries related to partial sums.
- Index entries related to q-numbers.
- Index entries for linear recurrences with constant coefficients, signature (37,-36).
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. A009980.
Programs
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Magma
[n le 2 select n-1 else 37*Self(n-1)-36*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
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Mathematica
LinearRecurrence[{37, -36}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *) Join[{0},Accumulate[36^Range[0,20]]] (* Harvey P. Dale, Jun 03 2015 *) -
Maxima
A218739(n):=(36^n-1)/35$ makelist(A218739(n),n,0,30); /* Martin Ettl, Nov 07 2012 */
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PARI
A218739(n)=36^n\35
Formula
From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1 - x)*(1 - 36*x)).
a(n) = 37*a(n-1) - 36*a(n-2).
a(n) = floor(36^n/35). (End)
E.g.f.: exp(x)*(exp(35*x) - 1)/35. - Stefano Spezia, Mar 28 2023
Comments