A255287
Number of 1's in expansion of F^n mod 3, where F = 1/(x*y)+1/y+x/y+1/x+x+y/x+y+x*y.
Original entry on oeis.org
1, 8, 8, 8, 64, 52, 8, 64, 101, 8, 64, 64, 64, 512, 404, 52, 416, 448, 8, 64, 233, 64, 512, 700, 101, 808, 992, 8, 64, 64, 64, 512, 416, 64, 512, 808, 64, 512, 512, 512, 4096, 3220, 404, 3232, 3224, 52, 416, 832, 416, 3328
Offset: 0
The pairs [no. of 1's, no. of 2's] are [1, 0], [8, 0], [8, 13], [8, 0], [64, 0], [52, 32], [8, 13], [64, 104], [101, 112], [8, 0], [64, 0], [64, 104], [64, 0], [512, 0], [404, 184], [52, 32], [416, 256], [448, 296], [8, 13], [64, 104], [233, 208], [64, 104], [512, 832], [700, 836], [101, 112], [808, 896], [992, 1081], ...
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# C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F1:=1/(x*y)+1/y+x/y+1/x+x+y/x+y+x*y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F1,n))[1],n=0..60)];
A255291
Number of 1's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.
Original entry on oeis.org
1, 5, 4, 5, 25, 12, 4, 20, 69, 5, 25, 20, 25, 125, 52, 12, 60, 281, 4, 20, 97, 20, 100, 353, 69, 345, 448, 5, 25, 20, 25, 125, 60, 20, 100, 345, 25, 125, 100, 125, 625, 252, 52, 260, 1341, 12, 60, 381, 60, 300, 1413, 281, 1405
Offset: 0
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], ...
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# C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F3:=1/x+1+x+1/y+y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F3,n))[1],n=0..60)];
A255292
Number of 2's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.
Original entry on oeis.org
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, 220, 573, 0, 0, 45, 0, 0, 185, 45, 225, 220, 0, 0, 225, 0, 0, 877, 177, 885, 716, 37, 185, 256, 185, 925, 788, 156, 780, 2281, 9
Offset: 0
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], ...
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# C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F3:=1/x+1+x+1/y+y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F3,n))[2],n=0..60)];
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