A218753 a(n) = (49^n - 1)/48.

0, 1, 50, 2451, 120100, 5884901, 288360150, 14129647351, 692352720200, 33925283289801, 1662338881200250, 81454605178812251, 3991275653761800300, 195572507034328214701, 9583052844682082520350, 469569589389422043497151, 23008909880081680131360400

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 49 (A087752).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries related to partial sums
• Index entries for linear recurrences with constant coefficients, signature (50,-49)

Crossrefs

Cf. A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218752, A133853, A094028, A218723.

Cf. A087752.

Programs

Magma

[n le 2 select n-1 else 50*Self(n-1) - 49*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 08 2012

Mathematica

LinearRecurrence[{50, -49}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)
Join[{0},Accumulate[49^Range[0,20]]] (* Harvey P. Dale, Apr 14 2023 *)

Maxima

A218753(n):=floor(49^n/48)$ makelist(A218753(n),n,0,30); /* Martin Ettl, Nov 05 2012 */

PARI

A218753(n)=49^n\48

Formula

G.f.: x/((1-x)*(1-49*x)). - Vincenzo Librandi, Nov 08 2012

a(n) = 50*a(n-1) - 49*a(n-2) with a(0)=0, a(1)=1. - Vincenzo Librandi, Nov 08 2012

a(n) = 49*a(n-1) + 1 with a(0)=0. - Vincenzo Librandi, Nov 08 2012

a(n) = floor(49^n/48). - Vincenzo Librandi, Nov 08 2012

E.g.f.: exp(25*x)*sinh(24*x)/24. - Elmo R. Oliveira, Aug 27 2024