cp's OEIS Frontend

A255291 Number of 1's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.

%I A255291 #7 Feb 21 2015 15:16:44
%S A255291 1,5,4,5,25,12,4,20,69,5,25,20,25,125,52,12,60,281,4,20,97,20,100,353,
%T A255291 69,345,448,5,25,20,25,125,60,20,100,345,25,125,100,125,625,252,52,
%U A255291 260,1341,12,60,381,60,300,1413,281,1405
%N A255291 Number of 1's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.
%C A255291 A255291 and A255292 together are a mod 3 analog of A072272.
%e A255291 The pairs [no. of 1's, no. of 2's] are [1, 0], [5, 0], [4, 9], [5, 0], [25, 0], [12, 37], [4, 9], [20, 45], [69, 44], [5, 0], [25, 0], [20, 45], [25, 0], [125, 0], [52, 177], [12, 37], [60, 185], [281, 156], [4, 9], [20, 45], [97, 72], [20, 45], [100, 225], [353, 228], [69, 44], [345, 220], [448, 573], [5, 0], [25, 0], [20, 45], ...
%p A255291 # C3 Counts 1's and 2's
%p A255291 C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
%p A255291 f2:=expand(f) mod 3; n1:=0; n2:=0;
%p A255291 if whattype(f2) = `+` then
%p A255291 t1:=nops(f2);
%p A255291 for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
%p A255291 c:=coeff(coeff(t2,x,ix),y,iy);
%p A255291 if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
%p A255291 else ix:=degree(f2, x); iy:=degree(f2, y);
%p A255291 c:=coeff(coeff(f2,x,ix),y,iy);
%p A255291 if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
%p A255291 fi;
%p A255291 end;
%p A255291 F3:=1/x+1+x+1/y+y mod 3;
%p A255291 g:=(F,n)->expand(F^n) mod 3;
%p A255291 [seq(C3(g(F3,n))[1],n=0..60)];
%Y A255291 Cf. A072272, A255288-A255294.
%K A255291 nonn
%O A255291 0,2
%A A255291 _N. J. A. Sloane_, Feb 21 2015