A218741 a(n) = (38^n - 1)/37.

0, 1, 39, 1483, 56355, 2141491, 81376659, 3092313043, 117507895635, 4465300034131, 169681401296979, 6447893249285203, 245019943472837715, 9310757851967833171, 353808798374777660499, 13444734338241551098963, 510899904853178941760595, 19414196384420799786902611

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 38 (A009982).

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 (39,-38).

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. A009982.

Programs

Magma

[n le 2 select n-1 else 39*Self(n-1) - 38*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{39, -38}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218741(n):=(38^n-1)/37$
makelist(A218741(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

A218741(n)=38^n\37

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-38*x)).

a(n) = 39*a(n-1) - 38*a(n-2).

a(n) = floor(38^n/37). (End)

E.g.f.: exp(x)*(exp(37*x) - 1)/37. - Elmo R. Oliveira, Aug 29 2024