login
a(n) + a(n - 1) is alternatively a cube or a square.
0

%I #13 Dec 12 2023 07:39:58

%S 1,7,2,6,3,5,4,4,5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,

%T 3,5,4,4,5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,3,5,4,4,

%U 5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,3,5,4,4,5,3,1,7,2,6,3

%N a(n) + a(n - 1) is alternatively a cube or a square.

%C a(1)=1, then a(2n) = (the least cube > a(2n-1)) - a(2n-1), and a(2n+1) = (the least square > a(2n)) - a(2n).

%C Period of length 10: {7,2,6,3,5,4,4,5,3,1}.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).

%F a(1)=1, afterwards a(n)=A130532(n+7).

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,1},{1,7,2,6,3,5,4,4,5,3},120] (* or *) PadRight[ {},120,{1,7,2,6,3,5,4,4,5,3}] (* _Harvey P. Dale_, Jul 05 2022 *)

%Y Cf. A130532.

%K nonn

%O 1,2

%A _Zak Seidov_, May 03 2010