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a(n) = (48^n - 1)/47.
3

%I #31 Aug 29 2024 19:56:49

%S 0,1,49,2353,112945,5421361,260225329,12490815793,599559158065,

%T 28778839587121,1381384300181809,66306446408726833,

%U 3182709427618887985,152770052525706623281,7332962521233917917489,351982201019228060039473,16895145648922946881894705,810966991148301450330945841

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

%C Partial sums of powers of 48 (A009992).

%H Vincenzo Librandi, <a href="/A218751/b218751.txt">Table of n, a(n) for n = 0..600</a>

%H <a href="/index/Par#partial">Index entries related to partial sums</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (49,-48).

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

%F From _Vincenzo Librandi_, Nov 08 2012: (Start)

%F G.f.: x/((1-x)*(1-48*x)).

%F a(n) = 49*a(n-1) - 48*a(n-2) with a(0)=0, a(1)=1.

%F a(n) = 48*a(n-1) + 1 with a(0)=0. (End)

%F E.g.f.: exp(x)*(exp(47*x) - 1)/47. - _Elmo R. Oliveira_, Aug 29 2024

%t LinearRecurrence[{49, -48}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)

%o (PARI) A218751(n)=48^n\47

%o (Maxima) A218751(n):=floor((48^n-1)/47)$ makelist(A218751(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */

%o (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

%Y 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.

%Y Cf. A009992.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012