A255294 Number of 2's in expansion of F^n mod 3, where F = 1/x+2+x+1/y+y.

0, 1, 5, 1, 8, 20, 5, 28, 64, 1, 8, 28, 8, 49, 101, 20, 109, 241, 5, 28, 80, 28, 149, 289, 64, 305, 437, 1, 8, 28, 8, 49, 109, 28, 149, 305, 8, 49, 149, 49, 272, 524, 101, 532, 1096, 20, 109, 305, 109, 572, 1096, 241, 1160

Offset

0,3

Comments

A255293 and A255294 together are a second mod 3 analog of A072272.

Links

Table of n, a(n) for n=0..52.

Example

The pairs [no. of 1's, no. of 2's] are [1, 0], [4, 1], [8, 5], [4, 1], [17, 8], [29, 20], [8, 5], [37, 28], [49, 64], [4, 1], [17, 8], [37, 28], [17, 8], [76, 49], [128, 101], [29, 20], [136, 109], [196, 241], [8, 5], [37, 28], [89, 80], [37, 28], [176, 149], [292, 289], [49, 64], [260, 305], [584, 437], [4, 1], [17, 8], [37, 28], ...

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;
F4:=1/x+2+x+1/y+y mod 3;
g:=(F, n)->expand(F^n) mod 3;
[seq(C3(g(F4, n))[2], n=0..60)];

Crossrefs

Cf. A072272, A255287-A255294.

Sequence in context: A193089 A154310 A193856 * A115521 A140705 A336053

Adjacent sequences: A255291 A255292 A255293 * A255295 A255296 A255297

Keyword

nonn

Author

N. J. A. Sloane, Feb 21 2015

Status

approved