A218749 a(n) = (46^n-1)/45.

0, 1, 47, 2163, 99499, 4576955, 210539931, 9684836827, 445502494043, 20493114725979, 942683277395035, 43363430760171611, 1994717814967894107, 91757019488523128923, 4220822896472063930459, 194157853237714940801115

Offset

0,3

Comments

Partial sums of powers of 46 (A009990).

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 (47,-46).

Formula

G.f.: x/((1-x)*(1-46*x)). - Vincenzo Librandi, Nov 08 2012

a(n) = 47*a(n-1) - 46*a(n-2) with a(0)=0, a(1)=1. - Vincenzo Librandi, Nov 08 2012

a(n) = 46*a(n-1) + 1 with a(0)=0. - Vincenzo Librandi, Nov 08 2012

a(n) = floor(46^n/45). - Vincenzo Librandi, Nov 08 2012

Mathematica

LinearRecurrence[{47, -46}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)
(46^Range[0, 20]-1)/45 (* Harvey P. Dale, Aug 17 2017 *)

Prog

(PARI) A218749(n)=46^n\45
(Maxima) A218749(n):=(46^n-1)/45$ makelist(A218749(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */
(Magma) [n le 2 select n-1 else 47*Self(n-1) - 46*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 08 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: A170680 A170728 A170766 * A049668 A009991 A052463

Adjacent sequences: A218746 A218747 A218748 * A218750 A218751 A218752

Keyword

nonn,easy

Author

M. F. Hasler, Nov 04 2012

Status

approved