A218751 a(n) = (48^n-1)/47.

0, 1, 49, 2353, 112945, 5421361, 260225329, 12490815793, 599559158065, 28778839587121, 1381384300181809, 66306446408726833, 3182709427618887985, 152770052525706623281, 7332962521233917917489, 351982201019228060039473

Offset

0,3

Comments

Partial sums of powers of 48 (A009992).

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 (49,-48).

Formula

a(n) = floor( 48^n/47 ).

G.f.: x/((1-x)*(1-48*x)). - Vincenzo Librandi, Nov 08 2012

a(n) = 49*a(n-1) - 48*a(n-2) with a(0)=0, a(1)=1. - Vincenzo Librandi, Nov 08 2012

a(n) = 48*a(n-1) + 1 with a(0)=0. - Vincenzo Librandi, Nov 08 2012

Mathematica

LinearRecurrence[{49, -48}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)

Prog

(PARI) A218751(n)=48^n\47
(Maxima) A218751(n):=floor((48^n-1)/47)$ makelist(A218751(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Magma) [n le 2 select n-1 else 49*Self(n-1)-48*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: A170682 A170730 A170768 * A120999 A087752 A069741

Adjacent sequences: A218748 A218749 A218750 * A218752 A218753 A218754

Keyword

nonn,easy

Author

M. F. Hasler, Nov 04 2012

Status

approved