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A245123
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Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 4.
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2
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2, 3, 9, 20, 46, 94, 202, 412, 850, 1719, 3483, 6987, 14026, 27990, 55830, 111022, 220589, 437451, 866898, 1715821, 3393973, 6708016, 13251455, 26163174, 51635765, 101868226, 200908954, 396129137, 780868821, 1538971204, 3032575428, 5974874666, 11770477038
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OFFSET
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11,1
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LINKS
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EXAMPLE
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a(11) = 2:
: o o :
: /( )\ / ( ) \ :
: o o o o o o o o :
: | | | ( ) | | :
: o o o o o o o :
: | | | | :
: o o o o :
: | :
: o :
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MAPLE
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b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
`if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
*b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
end:
A:= proc(n, k) option remember;
`if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
end:
a:= n-> b(n-1$2, 4$2):
seq(a(n), n=11..50);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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