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.

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

0,2

Comments

A255287 and A255288 together are a mod 3 analog of A160239.

Links

Table of n, a(n) for n=0..49.

Example

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], ...

Maple

# 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)];

Crossrefs

Cf. A160239, A255288-A255294.

Sequence in context: A242891 A266209 A077106 * A257342 A252850 A316163

Adjacent sequences: A255284 A255285 A255286 * A255288 A255289 A255290

Keyword

nonn

Author

N. J. A. Sloane, Feb 21 2015

Status

approved