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%I #16 Sep 08 2022 08:46:04
%S 0,1,45,1981,87165,3835261,168751485,7425065341,326702875005,
%T 14374926500221,632496766009725,27829857704427901,1224513738994827645,
%U 53878604515772416381,2370658598693986320765,104308978342535398113661
%N a(n) = (44^n-1)/43.
%C Partial sums of powers of 44 (A009988).
%H Vincenzo Librandi, <a href="/A218747/b218747.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 (45,-44)
%F G.f.: x/((1-x)*(1-44*x)). - _Vincenzo Librandi_, Nov 07 2012
%F a(n) = 45*a(n-1) - 44*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%F a(n) = floor(44^n/43). - _Vincenzo Librandi_, Nov 07 2012
%t LinearRecurrence[{45, -44}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t Join[{0},Accumulate[44^Range[0,20]]] (* _Harvey P. Dale_, Dec 28 2015 *)
%o (PARI) A218747(n)=44^n\43
%o (Magma) [n le 2 select n-1 else 45*Self(n-1) - 44*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o (Maxima) A218747(n):=(44^n-1)/43$
%o makelist(A218747(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.
%K nonn,easy
%O 0,3
%A _M. F. Hasler_, Nov 04 2012
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