A218740 a(n) = (37^n - 1)/36.

0, 1, 38, 1407, 52060, 1926221, 71270178, 2636996587, 97568873720, 3610048327641, 133571788122718, 4942156160540567, 182859777940000980, 6765811783780036261, 250335035999861341658, 9262396331994869641347, 342708664283810176729840, 12680220578500976539004081

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 37 (A009981).

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 (38,-37).

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. A009981.

Programs

Magma

[n le 2 select n-1 else 38*Self(n-1)-37*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{38, -37}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218740(n):=(37^n-1)/36$
makelist(A218740(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218740(n)=37^n\36

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1 - x)*(1 - 37*x)).

a(n) = 38*a(n-1) - 37*a(n-2).

a(n) = floor(37^n/36). (End)

E.g.f.: exp(x)*(exp(36*x) - 1)/36. - Stefano Spezia, Mar 28 2023