# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a218751 Showing 1-1 of 1 %I A218751 #31 Aug 29 2024 19:56:49 %S A218751 0,1,49,2353,112945,5421361,260225329,12490815793,599559158065, %T A218751 28778839587121,1381384300181809,66306446408726833, %U A218751 3182709427618887985,152770052525706623281,7332962521233917917489,351982201019228060039473,16895145648922946881894705,810966991148301450330945841 %N A218751 a(n) = (48^n - 1)/47. %C A218751 Partial sums of powers of 48 (A009992). %H A218751 Vincenzo Librandi, Table of n, a(n) for n = 0..600 %H A218751 Index entries related to partial sums. %H A218751 Index entries for linear recurrences with constant coefficients, signature (49,-48). %F A218751 a(n) = floor(48^n/47). %F A218751 From _Vincenzo Librandi_, Nov 08 2012: (Start) %F A218751 G.f.: x/((1-x)*(1-48*x)). %F A218751 a(n) = 49*a(n-1) - 48*a(n-2) with a(0)=0, a(1)=1. %F A218751 a(n) = 48*a(n-1) + 1 with a(0)=0. (End) %F A218751 E.g.f.: exp(x)*(exp(47*x) - 1)/47. - _Elmo R. Oliveira_, Aug 29 2024 %t A218751 LinearRecurrence[{49, -48}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 08 2012 *) %o A218751 (PARI) A218751(n)=48^n\47 %o A218751 (Maxima) A218751(n):=floor((48^n-1)/47)$ makelist(A218751(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */ %o A218751 (Magma) [n le 2 select n-1 else 49*Self(n-1)-48*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2012 %Y A218751 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 A218751 Cf. A009992. %K A218751 nonn,easy %O A218751 0,3 %A A218751 _M. F. Hasler_, Nov 04 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE