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

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

Offset

0,3

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).

Formula

G.f.: x/((1-x)*(1-38*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 39*a(n-1) - 38*a(n-2). - Vincenzo Librandi, Nov 07 2012

a(n) = floor(38^n/37). - Vincenzo Librandi, Nov 07 2012

Mathematica

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

Prog

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

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.

Sequence in context: A170672 A170720 A170758 * A112617 A009983 A269028

Adjacent sequences: A218738 A218739 A218740 * A218742 A218743 A218744

Keyword

nonn,easy

Author

M. F. Hasler, Nov 04 2012

Status

approved