A255289 Number of 1's in expansion of F^n mod 3, where F = 1/(x*y)+2/y+x/y+2/x+2*x+y/x+2*y+x*y.

1, 4, 12, 4, 32, 48, 12, 84, 117, 4, 32, 84, 32, 256, 300, 48, 336, 324, 12, 84, 225, 84, 672, 792, 117, 852, 876, 4, 32, 84, 32, 256, 336, 84, 672, 852, 32, 256, 672, 256, 2048, 2316, 300, 2352, 2448, 48, 336, 900, 336

Offset

0,2

Comments

A255289 and A255290 together are a second mod 3 analog of A160239.

Links

Table of n, a(n) for n=0..48.

Example

The pairs [no. of 1's, no. of 2's] are [1, 0], [4, 4], [12, 9], [4, 4], [32, 32], [48, 36], [12, 9], [84, 84], [117, 96], [4, 4], [32, 32], [84, 84], [32, 32], [256, 256], [300, 288], [48, 36], [336, 336], [324, 420], [12, 9], [84, 84], [225, 216], [84, 84], [672, 672], [792, 744], [117, 96], [852, 852], [876, 1197], ...

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;
F2:=1/(x*y)+2/y+x/y+2/x+2*x+y/x+2*y+x*y mod 3;
g:=(F, n)->expand(F^n) mod 3;
[seq(C3(g(F2, n))[1], n=0..60)];

Crossrefs

Cf. A160239, A255287-A255294.

Sequence in context: A084351 A286682 A262621 * A348334 A337403 A203031

Adjacent sequences: A255286 A255287 A255288 * A255290 A255291 A255292

Keyword

nonn

Author

N. J. A. Sloane, Feb 21 2015

Status

approved