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A255290 Number of 2'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. 2
0, 4, 9, 4, 32, 36, 9, 84, 96, 4, 32, 84, 32, 256, 288, 36, 336, 420, 9, 84, 216, 84, 672, 744, 96, 852, 1197, 4, 32, 84, 32, 256, 336, 84, 672, 852, 32, 256, 672, 256, 2048, 2304, 288, 2352, 2544, 36, 336, 864, 336, 2688 (list; graph; refs; listen; history; text; internal format)
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..49.

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

CROSSREFS

Cf. A160239, A255287-A255294.

Sequence in context: A053143 A068238 A280441 * A087369 A200629 A021206

Adjacent sequences:  A255287 A255288 A255289 * A255291 A255292 A255293

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 21 2015

STATUS

approved

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Last modified February 17 18:37 EST 2020. Contains 332005 sequences. (Running on oeis4.)