A218727 - OEIS

%I #20 Aug 29 2024 17:03:49

%S 0,1,25,601,14425,346201,8308825,199411801,4785883225,114861197401,

%T 2756668737625,66160049703001,1587841192872025,38108188628928601,

%U 914596527094286425,21950316650262874201,526807599606308980825,12643382390551415539801,303441177373233972955225

%N a(n) = (24^n - 1)/23.

%C Partial sums of powers of 24 (A009968); q-integers for q=24: diagonal k=1 in triangle A022188.

%C Partial sums are in A014913. Also, the sequence is related to A014942 by A014942(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. [_Bruno Berselli_, Nov 07 2012]

%H Vincenzo Librandi, <a href="/A218727/b218727.txt">Table of n, a(n) for n = 0..700</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 (25,-24).

%F From _Vincenzo Librandi_, Nov 07 2012: (Start)

%F G.f.: x/((1-x)*(1-24*x)).

%F a(n) = floor(24^n/23).

%F a(n) = 25*a(n-1) - 24*a(n-2). (End)

%F E.g.f.: exp(x)*(exp(23*x) - 1)/23. - _Elmo R. Oliveira_, Aug 29 2024

%t LinearRecurrence[{25, -24}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)

%o (PARI) A218727(n)=24^n\23

%o (Magma) [n le 2 select n-1 else 25*Self(n-1)-24*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012

%o (Maxima) A218727(n):=(24^n-1)/23$

%o makelist(A218727(n),n,0,30); /* _Martin Ettl_, Nov 07 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. A009968, A014942, A022188.

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, Nov 04 2012