This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218746 #21 Aug 27 2024 18:55:32
%S A218746 0,1,44,1893,81400,3500201,150508644,6471871693,278290482800,
%T A218746 11966490760401,514559102697244,22126041415981493,951419780887204200,
%U A218746 40911050578149780601,1759175174860440565844,75644532518998944331293,3252714898316954606245600,139866740627629048068560801
%N A218746 a(n) = (43^n - 1)/42.
%C A218746 Partial sums of powers of 43 (A009987).
%C A218746 0 followed by the binomial transform of A170762. - _R. J. Mathar_, Jul 18 2015
%H A218746 Vincenzo Librandi, <a href="/A218746/b218746.txt">Table of n, a(n) for n = 0..600</a>
%H A218746 <a href="/index/Par#partial">Index entries related to partial sums</a>
%H A218746 <a href="/index/Q#q-numbers">Index entries related to q-numbers</a>
%H A218746 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (44,-43)
%F A218746 G.f.: x/((1-x)*(1-43*x)). - _Vincenzo Librandi_, Nov 07 2012
%F A218746 a(n) = 44*a(n-1) - 43*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%F A218746 a(n) = floor(43^n/42). - _Vincenzo Librandi_, Nov 07 2012
%F A218746 E.g.f.: exp(22*x)*sinh(21*x)/21. - _Elmo R. Oliveira_, Aug 27 2024
%t A218746 LinearRecurrence[{44, -43}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218746 Join[{0},Accumulate[43^Range[0,20]]] (* _Harvey P. Dale_, Jan 27 2015 *)
%o A218746 (PARI) A218746(n)=43^n\42
%o A218746 (Magma) [n le 2 select n-1 else 44*Self(n-1) - 43*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218746 (Maxima) A218746(n):=(43^n-1)/42$
%o A218746 makelist(A218746(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218746 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 A218746 Cf. A009987, A170762.
%K A218746 nonn,easy
%O A218746 0,3
%A A218746 _M. F. Hasler_, Nov 04 2012