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A271362
Number T(n,k) of series-reduced free trees with n nodes of which exactly k>=3 are leaves, k+1 <= n <= 2k-2.
2
1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 4, 3, 1, 4, 6, 3, 1, 2, 10, 9, 4, 1, 8, 17, 12, 4, 1, 4, 22, 30, 16, 5, 1, 15, 47, 44, 20, 5, 1, 6, 53, 91, 67, 25, 6, 1, 32, 127, 158, 91, 30, 6, 1, 11, 121, 282, 258, 126
OFFSET
4,8
COMMENTS
The length of row n is floor((n-2)/2).
FORMULA
T(n,k) = A271205(k,n).
EXAMPLE
Irregular triangle begins
n \ k 3 4 5 6 7 8
4 1;
5 1;
6 1, 1;
7 1, 1;
8 1, 2, 1;
9 2, 2, 1;
10 2, 4, 3, 1;
11 4, 6, 3, 1;
12 2, 10, 9, 4, 1;
13 8, 17, 12, 4, 1;
14 4, 22, 30, 16, 5, 1;
15 15, 47, 44, 20, 5, 1;
...
PROG
(PARI) \\ using files hitree4.txt etc from McKay.
nL(n, Tr) = { my(E = strsplit(Tr, " "), u_v, Deg = vectorsmall(n));
for(j = 1, n-1, u_v = strsplit(E[j], " "); u_v = eval(u_v);
Deg[ u_v[1]+1 ]++; Deg[ u_v[2]+1 ]++); sum(v = 1, n, Deg[v] == 1)
};
Rows(r1, r2) = {my(F, C, nF); for(n = r1, r2,
F = readstr(Str("hitree", n, ".txt")); C = vectorsmall(n-1);
for(i = 1, #F, nF = nL(n, F[i]); C[nF]++ );
print1(n" "); for(i=1, #C, if(C[i] > 0, print1(C[i]", "))); print() )
}; Washington Bomfim, Jul 09 2021
CROSSREFS
Transpose of A271205.
Cf. A000014 (row sums), A345971.
Sequence in context: A355395 A107030 A371692 * A354555 A263643 A336534
KEYWORD
nonn,tabf
AUTHOR
Stephan Beyer, Apr 05 2016
STATUS
approved