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A218722 a(n) = (19^n-1)/18.

%I A218722 #38 Mar 13 2023 02:59:23
%S A218722 0,1,20,381,7240,137561,2613660,49659541,943531280,17927094321,
%T A218722 340614792100,6471681049901,122961939948120,2336276859014281,
%U A218722 44389260321271340,843395946104155461,16024522975978953760,304465936543600121441
%N A218722 a(n) = (19^n-1)/18.
%C A218722 Partial sums of powers of 19 (A001029); q-integers for q=19: diagonal k=1 in triangle A022183.
%C A218722 Partial sums are in A014903. Also, the sequence is related to A014936 by A014936(n) = n*a(n)-sum(a(i), i=0..n-1) for n>0. - _Bruno Berselli_, Nov 06 2012
%H A218722 Vincenzo Librandi, <a href="/A218722/b218722.txt">Table of n, a(n) for n = 0..700</a>
%H A218722 <a href="/index/Par#partial">Index entries related to partial sums</a>
%H A218722 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-19).
%F A218722 a(n) = floor(19^n/18).
%F A218722 G.f.: x/((1-x)*(1-19*x)). - _Bruno Berselli_, Nov 06 2012
%F A218722 a(n) = 20*a(n-1) - 19*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%F A218722 E.g.f.: exp(10*x)*sinh(9*x)/9. - _Stefano Spezia_, Mar 11 2023
%t A218722 LinearRecurrence[{20, -19}, {0, 1}, 40] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o A218722 (PARI) A218722(n)=19^n\18
%o A218722 (Maxima) A218722(n):=(19^n-1)/18$ makelist(A218722(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A218722 (Magma) [n le 2 select n-1 else 20*Self(n-1)-19*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%Y A218722 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, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.
%Y A218722 Cf. A001029, A014903, A014936, A022183.
%K A218722 nonn,easy
%O A218722 0,3
%A A218722 _M. F. Hasler_, Nov 04 2012