A017000 - OEIS

%I #18 Sep 08 2022 08:44:41

%S 1,16777216,2562890625,54875873536,500246412961,2821109907456,

%T 11688200277601,39062500000000,111429157112001,281474976710656,

%U 645753531245761,1370114370683136,2724905250390625,5132188731375616

%N a(n) = (7*n + 1)^8.

%H Vincenzo Librandi, <a href="/A017000/b017000.txt">Table of n, a(n) for n = 0..10000</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(0)=1, a(1)=16777216, a(2)=2562890625, a(3)=54875873536, a(4)=500246412961, a(5)=2821109907456, a(6)=11688200277601, a(7)=39062500000000, a(8)=111429157112001, a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - _Harvey P. Dale_, Mar 30 2012

%F a(n) = 1679616 - 15676416*n + 64012032*n^2 - 149361408*n^3 + 217818720*n^4 - 203297472*n^5 + 118590192*n^6 - 39530064*n^7 + 5764801*n^8. - _Harvey P. Dale_, Mar 30 2012

%t (7*Range[0,30]+1)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,16777216,2562890625,54875873536,500246412961,2821109907456,11688200277601,39062500000000,111429157112001},30] (* _Harvey P. Dale_, Mar 30 2012 *)

%o (Magma) [(7*n+1)^8: n in [0..20]]; // _Vincenzo Librandi_, Jul 13 2011

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_