A297964 - OEIS

%I #6 Jan 11 2018 23:46:32

%S 1,-2,2,1,0,-1,-2,-3,-3,-2,-2,-1,-1,0,0,1,1,2,2,3,2,2,3,2,1,1,2,1,1,2,

%T 1,0,0,1,0,0,1,0,-1,-1,0,-1,-1,0,-1,-2,-2,-1,-2,-2,-1,-2,-3,-3,-2,-3,

%U -3,-2,-3,-4,-4,-3,-3,-2,-3,-3,-2,-3,-4,-4,-3,-3

%N a(n) = A296220(n) - 4n.

%C It has been checked that -9 <= a(n) <= 8 for n=1..6*10^6. Conjectures: every integer appears infinitely many times, and -2 < a(n) - a(n-1) < 2 for n > 2.

%H Clark Kimberling, <a href="/A297964/b297964.txt">Table of n, a(n) for n = 0..10000</a>

%t a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;

%t a[n_] := a[n] = a[0]*b[n - 1] + a[1]*b[n - 2];

%t j = 1; While[j < 20000, k = a[j] - j - 1;

%t While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++];

%t Table[a[n], {n, 0, k}]; (* A296220 *)

%t Take[Table[a[n] - 4 n, {n, 0, k}], 300] (* A297964 *)

%Y Cf. A296220.

%K sign,easy

%O 0,2

%A _Clark Kimberling_, Jan 10 2018