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A323598 "Word binomial coefficient" for (x|y) where y is the first n symbols of the Thue-Morse sequence (A010060) and x is the first 2n symbols. 2
1, 1, 2, 3, 7, 15, 32, 52, 126, 225, 554, 995, 2446, 5386, 11808, 19869, 49025, 109837, 245854, 425227, 1064505, 2413233, 5466912, 9592348, 24178488, 45073812, 113262740, 208166868, 518091370, 1155428876, 2571714336, 4419410606, 11038230966, 20406919817 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The "word binomial coefficient" (x|y) is the number of ways that y can be a (scattered) subsequence of x.

LINKS

Robert Israel, Table of n, a(n) for n = 0..200

EXAMPLE

a(4) = 7 because there are 7 ways 0110 can be a subsequence of 01101001.

MAPLE

f:= proc(x, y)

     option remember;

     local n, m, Res, L, j, t;

     n:= nops(x); m:= nops(y);

     if n < m then return 0

     elif n = m then if x = y then return 1 else return 0 fi

     elif m = 0 then return 1 fi;

     L:= select(j -> x[j] = y[1], [$1..n-m+1]);

     add(procname(x[j+1..-1], y[2..-1]), j=L);

end proc:

TM:= StringTools[Explode](StringTools:-ThueMorse(200)):

seq(f(TM[1..2*n], TM[1..n]), n=0..100); # Robert Israel, Jan 20 2019

CROSSREFS

Cf. A010060, A323597.

Sequence in context: A153010 A076993 A076698 * A078007 A198683 A001932

Adjacent sequences:  A323595 A323596 A323597 * A323599 A323600 A323601

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Jan 18 2019

STATUS

approved

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Last modified August 14 01:55 EDT 2020. Contains 336476 sequences. (Running on oeis4.)