A255291 - OEIS

A255291

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

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

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OFFSET

0,2

COMMENTS

A255291 and A255292 together are a 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], [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], ...

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;

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)];

CROSSREFS

Cf. A072272, A255288-A255294.

Sequence in context: A184306 A176317 A092426 * A070365 A368666 A190613

Adjacent sequences: A255288 A255289 A255290 * A255292 A255293 A255294

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 21 2015

STATUS

approved