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

0,3

Comments

Partial sums of powers of 36 (A009980).

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).

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

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 *)

Prog

(PARI) A218739(n)=36^n\35
(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
(Maxima) A218739(n):=(36^n-1)/35$
makelist(A218739(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.

Cf. A009980.

Sequence in context: A170670 A170718 A170756 * A217961 A263372 A206565

Adjacent sequences: A218736 A218737 A218738 * A218740 A218741 A218742

Keyword

nonn,easy

Author

M. F. Hasler, Nov 04 2012

Status

approved