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%I A218725 #25 Aug 29 2024 17:03:34
%S A218725 0,1,23,507,11155,245411,5399043,118778947,2613136835,57489010371,
%T A218725 1264758228163,27824681019587,612142982430915,13467145613480131,
%U A218725 296277203496562883,6518098476924383427,143398166492336435395,3154759662831401578691,69404712582290834731203
%N A218725 a(n) = (22^n - 1)/21.
%C A218725 Partial sums of powers of 22; q-integers for q=22: Diagonal k=1 in the triangle A022186.
%C A218725 Partial sums are in A014907. Also, the sequence is related to A014940 by A014940(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. [_Bruno Berselli_, Nov 06 2012]
%H A218725 Vincenzo Librandi, <a href="/A218725/b218725.txt">Table of n, a(n) for n = 0..700</a>
%H A218725 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218725 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (23,-22).
%F A218725 a(n) = floor(22^n/21).
%F A218725 G.f.: x/((1-x)*(1-22*x)). [_Bruno Berselli_, Nov 06 2012]
%F A218725 a(n) = 23*a(n-1) - 22*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%F A218725 E.g.f.: exp(x)*(exp(21*x) - 1)/21. - _Elmo R. Oliveira_, Aug 29 2024
%t A218725 LinearRecurrence[{23, -22}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o A218725 (PARI) A218725(n)=22^n\21
%o A218725 (Maxima) A218725(n):=(22^n-1)/21$ makelist(A218725(n),n,0,30); /* _Martin Ettl_, Nov 06 2012 */
%o A218725 (Magma) [n le 2 select n-1 else 23*Self(n-1) - 22*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%Y A218725 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 A218725 Cf. A014907, A014940, A022186.
%K A218725 nonn,easy
%O A218725 0,3
%A A218725 _M. F. Hasler_, Nov 04 2012

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