login
a(n) = n^9 - n^8.
4

%I #32 Feb 09 2024 12:39:07

%S 0,0,256,13122,196608,1562500,8398080,34588806,117440512,344373768,

%T 900000000,2143588810,4729798656,9788768652,19185257728,35880468750,

%U 64424509440,111612119056,187339329792,305704134738,486400000000,756457187220,1152393344256,1722841676182

%N a(n) = n^9 - n^8.

%C For n>1 number of 9-digit positive integers in base n.

%H Vincenzo Librandi, <a href="/A240932/b240932.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n) = n^8*(n-1) = n^9 - n^8.

%F a(n) = A001017(n) - A001016(n).

%F G.f.: 2*x^2*(x^7+374*x^6+9327*x^5+49780*x^4+78095*x^3+38454*x^2+5281*x+128) / (x-1)^10. - _Colin Barker_, Aug 08 2014

%F Sum_{n>=2} 1/a(n) = 8 - Sum_{k=2..8} zeta(k). - _Amiram Eldar_, Jul 05 2020

%t Table[n^9 - n^8, {n, 0, 40}] (* _Vincenzo Librandi_, Aug 15 2016 *)

%o (PARI) vector(100, n, (n-1)^9 - (n-1)^8) \\ _Derek Orr_, Aug 03 2014

%o (Magma) [n^9-n^8: n in [0..40]]; // _Vincenzo Librandi_, Aug 15 2016

%Y Cf. A001016, A001017.

%Y Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240931, A240933.

%K nonn,easy

%O 0,3

%A _Martin Renner_, Aug 03 2014