A240931 - OEIS

%I #41 Sep 08 2022 08:46:07

%S 0,0,128,4374,49152,312500,1399680,4941258,14680064,38263752,90000000,

%T 194871710,394149888,752982204,1370375552,2392031250,4026531840,

%U 6565418768,10407740544,16089691302,24320000000,36021770820,52381515648,74906159834,105488842752,146484375000

%N a(n) = n^8 - n^7.

%C For n>1 number of 8-digit positive integers in base n.

%H Vincenzo Librandi, <a href="/A240931/b240931.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F a(n) = n^7*(n-1) = n^8 - n^7.

%F a(n) = A001016(n) - A001015(n).

%F G.f.: -2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9. - _Colin Barker_, Aug 08 2014

%F Sum_{n>=2} 1/a(n) = 7 - Sum_{k=2..7} zeta(k). - _Amiram Eldar_, Jul 05 2020

%p A240931:=n->n^8-n^7: seq(A240931(n), n=0..30); # _Wesley Ivan Hurt_, Aug 09 2014

%t Table[n^8 - n^7, {n, 0, 30}] (* _Wesley Ivan Hurt_, Aug 09 2014 *)

%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,0,128,4374,49152,312500,1399680,4941258,14680064},30] (* _Harvey P. Dale_, Apr 29 2016 *)

%o (PARI) vector(100, n, (n-1)^8 - (n-1)^7) \\ _Derek Orr_, Aug 03 2014

%o (PARI) concat([0,0], Vec(-2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9 + O(x^100))) \\ _Colin Barker_, Aug 08 2014

%o (Magma) [n^8-n^7 : n in [0..30]]; // _Wesley Ivan Hurt_, Aug 09 2014

%Y Cf. A001015, A001016.

%Y Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240932, A240933.

%K nonn,easy

%O 0,3

%A _Martin Renner_, Aug 03 2014