A255293 - OEIS

%I #9 Feb 21 2015 15:25:59

%S 1,4,8,4,17,29,8,37,49,4,17,37,17,76,128,29,136,196,8,37,89,37,176,

%T 292,49,260,584,4,17,37,17,76,136,37,176,260,17,76,176,76,353,605,128,

%U 613,961,29,136,332,136,653,1105,196

%N Number of 1's in expansion of F^n mod 3, where F = 1/x+2+x+1/y+y.

%C A255293 and A255294 together are a second mod 3 analog of A072272.

%e The pairs [no. of 1's, no. of 2's] are [1, 0], [4, 1], [8, 5], [4, 1], [17, 8], [29, 20], [8, 5], [37, 28], [49, 64], [4, 1], [17, 8], [37, 28], [17, 8], [76, 49], [128, 101], [29, 20], [136, 109], [196, 241], [8, 5], [37, 28], [89, 80], [37, 28], [176, 149], [292, 289], [49, 64], [260, 305], [584, 437], [4, 1], [17, 8], [37, 28], ...

%p # C3 Counts 1's and 2's

%p C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;

%p f2:=expand(f) mod 3; n1:=0; n2:=0;

%p if whattype(f2) = `+` then

%p t1:=nops(f2);

%p for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);

%p c:=coeff(coeff(t2,x,ix),y,iy);

%p if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);

%p else ix:=degree(f2, x); iy:=degree(f2, y);

%p c:=coeff(coeff(f2,x,ix),y,iy);

%p if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);

%p fi;

%p end;

%p F4:=1/x+2+x+1/y+y mod 3;

%p g:=(F,n)->expand(F^n) mod 3;

%p [seq(C3(g(F4,n))[1],n=0..60)];

%Y Cf. A072272, A255287-A255294.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Feb 21 2015