cp's OEIS Frontend

A255292 Number of 2's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.

%I A255292 #6 Feb 21 2015 15:20:41
%S A255292 0,0,9,0,0,37,9,45,44,0,0,45,0,0,177,37,185,156,9,45,72,45,225,228,44,
%T A255292 220,573,0,0,45,0,0,185,45,225,220,0,0,225,0,0,877,177,885,716,37,185,
%U A255292 256,185,925,788,156,780,2281,9
%N A255292 Number of 2's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.
%C A255292 A255291 and A255292 together are a mod 3 analog of A072272.
%e A255292 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 A255292 # C3 Counts 1's and 2's
%p A255292 C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
%p A255292 f2:=expand(f) mod 3; n1:=0; n2:=0;
%p A255292 if whattype(f2) = `+` then
%p A255292 t1:=nops(f2);
%p A255292 for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
%p A255292 c:=coeff(coeff(t2,x,ix),y,iy);
%p A255292 if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
%p A255292 else ix:=degree(f2, x); iy:=degree(f2, y);
%p A255292 c:=coeff(coeff(f2,x,ix),y,iy);
%p A255292 if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
%p A255292 fi;
%p A255292 end;
%p A255292 F3:=1/x+1+x+1/y+y mod 3;
%p A255292 g:=(F,n)->expand(F^n) mod 3;
%p A255292 [seq(C3(g(F3,n))[2],n=0..60)];
%Y A255292 Cf. A072272, A255288-A255294.
%K A255292 nonn
%O A255292 0,3
%A A255292 _N. J. A. Sloane_, Feb 21 2015