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A218750 a(n) = (47^n-1)/46. 4

%I

%S 0,1,48,2257,106080,4985761,234330768,11013546097,517636666560,

%T 24328923328321,1143459396431088,53742591632261137,

%U 2525901806716273440,118717384915664851681,5579717091036248029008,262246703278703657363377

%N a(n) = (47^n-1)/46.

%C Partial sums of powers of 47 (A009991).

%H Vincenzo Librandi, <a href="/A218750/b218750.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/Q#q-numbers">Index entries related to q-numbers</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (48,-47)

%F a(n) = floor(47^n/46).

%F G.f.: x/(47*x^2-48*x+1) = x/((1-x)*(1-47*x)). [_Colin Barker_, Nov 06 2012]

%F a(0)=0, a(n) = 47*a(n-1) + 1. - _Vincenzo Librandi_, Nov 08 2012

%t Table[(47^n - 1)/46, {n, 0, 19}] (* _Alonso del Arte_, Nov 04 2012 *)

%t LinearRecurrence[{48, -47}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)

%o (PARI) A218750(n)=47^n\46

%o (Maxima) A218750(n):=(47^n-1)/46$ makelist(A218750(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */

%o (MAGMA) [n le 2 select n-1 else 48*Self(n-1) - 47*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.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012

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Last modified May 21 08:53 EDT 2019. Contains 323441 sequences. (Running on oeis4.)