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A218745 a(n) = (42^n - 1)/41.

%I A218745 #20 Aug 29 2024 16:00:28
%S A218745 0,1,43,1807,75895,3187591,133878823,5622910567,236162243815,
%T A218745 9918814240231,416590198089703,17496788319767527,734865109430236135,
%U A218745 30864334596069917671,1296302053034936542183,54444686227467334771687,2286676821553628060410855,96040426505252378537255911
%N A218745 a(n) = (42^n - 1)/41.
%C A218745 Partial sums of powers of 42 (A009986).
%H A218745 Vincenzo Librandi, <a href="/A218745/b218745.txt">Table of n, a(n) for n = 0..600</a>
%H A218745 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218745 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>.
%H A218745 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (43,-42).
%F A218745 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218745 G.f.: x/((1-x)*(1-42*x)).
%F A218745 a(n) = 43*a(n-1) - 42*a(n-2).
%F A218745 a(n) = floor(42^n/41). (End)
%F A218745 E.g.f.: exp(x)*(exp(41*x) - 1)/41. - _Elmo R. Oliveira_, Aug 29 2024
%t A218745 LinearRecurrence[{43, -42}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218745 (42^Range[0,20]-1)/41 (* _Harvey P. Dale_, May 08 2024 *)
%o A218745 (PARI) A218745(n)=42^n\41
%o A218745 (Magma) [n le 2 select n-1 else 43*Self(n-1) - 42*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218745 (Maxima) A218745(n):=(42^n-1)/41$
%o A218745 makelist(A218745(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218745 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 A218745 Cf. A009986.
%K A218745 nonn,easy
%O A218745 0,3
%A A218745 _M. F. Hasler_, Nov 04 2012