A240933 - OEIS

%I #34 Feb 09 2024 12:39:02

%S 0,0,512,39366,786432,7812500,50388480,242121642,939524096,3099363912,

%T 9000000000,23579476910,56757583872,127253992476,268593608192,

%U 538207031250,1030792151040,1897406023952,3372107936256,5808378560022,9728000000000,15885600931620,25352653573632

%N a(n) = n^10 - n^9.

%C For n>1 number of 10-digit positive integers in base n.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F a(n) = n^9*(n-1) = n^10 - n^9.

%F a(n) = A008454(n) - A001017(n). - _Michel Marcus_, Aug 03 2014

%F G.f.: 2*(256*x^2 + 16867*x^3 + 190783*x^4 + 621199*x^5 + 689155*x^6 + 264409*x^7 + 30973*x^8 + 757*x^9 + x^10)/(1 - x)^11. - _Wesley Ivan Hurt_, Aug 03 2014

%F Recurrence: a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). - _Wesley Ivan Hurt_, Aug 03 2014

%F Sum_{n>=2} 1/a(n) = 9 - Sum_{k=2..9} zeta(k). - _Amiram Eldar_, Jul 05 2020

%p A240933:=n->n^10-n^9: seq(A240933(n), n=0..30); # _Wesley Ivan Hurt_, Aug 03 2014

%t Table[n^10 - n^9, {n, 0, 30}] (* _Wesley Ivan Hurt_, Aug 03 2014 *)

%t CoefficientList[Series[2 (256*x^2 + 16867*x^3 + 190783*x^4 + 621199*x^5 + 689155*x^6 + 264409*x^7 + 30973*x^8 + 757*x^9 + x^10)/(1 - x)^11, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Aug 03 2014 *)

%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,0,512,39366,786432,7812500,50388480,242121642,939524096,3099363912,9000000000},40] (* _Harvey P. Dale_, Oct 19 2022 *)

%o (PARI) vector(100, n, (n-1)^10 - (n-1)^9) \\ _Derek Orr_, Aug 03 2014

%o (Magma) [n^10-n^9 : n in [0..30]]; // _Wesley Ivan Hurt_, Aug 03 2014

%Y Cf. A001017, A008454.

%Y Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240931, A240932.

%K nonn,easy

%O 0,3

%A _Martin Renner_, Aug 03 2014