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A218748 a(n) = (45^n - 1)/44.

%I A218748 #30 Aug 27 2024 19:18:20
%S A218748 0,1,46,2071,93196,4193821,188721946,8492487571,382161940696,
%T A218748 17197287331321,773877929909446,34824506845925071,1567102808066628196,
%U A218748 70519626362998268821,3173383186334922096946,142802243385071494362571,6426100952328217246315696
%N A218748 a(n) = (45^n - 1)/44.
%C A218748 Partial sums of powers of 45 (A009989).
%H A218748 Vincenzo Librandi, <a href="/A218748/b218748.txt">Table of n, a(n) for n = 0..600</a>
%H A218748 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218748 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.
%H A218748 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (46,-45).
%F A218748 G.f.: x/((1-x)*(1-45*x)). - _Vincenzo Librandi_, Nov 08 2012
%F A218748 a(n) = 46*a(n-1) - 45*a(n-2) with a(0)=0, a(1)=1. - _Vincenzo Librandi_, Nov 08 2012
%F A218748 a(n) = 45*a(n-1) + 1 with a(0)=0. - _Vincenzo Librandi_, Nov 08 2012
%F A218748 a(n) = floor(45^n/44).  - _Vincenzo Librandi_, Nov 08 2012
%F A218748 E.g.f.: exp(23*x)*sinh(22*x)/22. - _Elmo R. Oliveira_, Aug 27 2024
%t A218748 LinearRecurrence[{46, -45}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *)
%o A218748 (PARI) A218748(n)=45^n\44
%o A218748 (Maxima) A218748(n):=(45^n-1)/44$ makelist(A218748(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%o A218748 (Magma) [n le 2 select n-1 else 46*Self(n-1) - 45*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2012
%Y A218748 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 A218748 Cf. A009989.
%K A218748 nonn,easy
%O A218748 0,3
%A A218748 _M. F. Hasler_, Nov 04 2012