# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a218744 Showing 1-1 of 1 %I A218744 #20 Aug 27 2024 21:47:23 %S A218744 0,1,42,1723,70644,2896405,118752606,4868856847,199623130728, %T A218744 8184548359849,335566482753810,13758225792906211,564087257509154652, %U A218744 23127577557875340733,948230679872888970054,38877457874788447772215,1593975772866326358660816,65353006687519380705093457 %N A218744 a(n) = (41^n - 1)/40. %C A218744 Partial sums of powers of 41 (A009985). %H A218744 Vincenzo Librandi, Table of n, a(n) for n = 0..600 %H A218744 Index entries related to partial sums. %H A218744 Index entries for linear recurrences with constant coefficients, signature (42,-41). %F A218744 a(n) = floor(41^n/40). %F A218744 G.f.: x/((1-x)*(1-41*x)). - _Vincenzo Librandi_, Nov 07 2012 %F A218744 a(n) = 42*a(n-1) - 41*a(n-2). - _Vincenzo Librandi_, Nov 07 2012 %F A218744 E.g.f.: exp(21*x)*sinh(20*x)/20. - _Elmo R. Oliveira_, Aug 27 2024 %t A218744 LinearRecurrence[{42, -41}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *) %o A218744 (PARI) A218744(n)=41^n\40 %o A218744 (Magma) [n le 2 select n-1 else 42*Self(n-1)-41*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012 %o A218744 (Maxima) A218744(n):=(41^n-1)/40$ %o A218744 makelist(A218744(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */ %Y A218744 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 A218744 Cf. A009985. %K A218744 nonn,easy %O A218744 0,3 %A A218744 _M. F. Hasler_, Nov 04 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE