A255288 - OEIS

A255288

Number of 2'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.

0, 0, 13, 0, 0, 32, 13, 104, 112, 0, 0, 104, 0, 0, 184, 32, 256, 296, 13, 104, 208, 104, 832, 836, 112, 896, 1081, 0, 0, 104, 0, 0, 256, 104, 832, 896, 0, 0, 832, 0, 0, 1400, 184, 1472, 1768, 32, 256, 932, 256, 2048, 2692, 296

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OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..51.

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))[2], n=0..60)];

CROSSREFS

Cf. A160239, A255287-A255294.

Sequence in context: A200065 A067155 A277255 * A221341 A221106 A271075

Adjacent sequences: A255285 A255286 A255287 * A255289 A255290 A255291

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 21 2015

STATUS

approved