

A026105


Triangle T read by rows: differences of Motzkin triangle (A026300).


15



1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 3, 6, 7, 5, 1, 4, 10, 16, 18, 12, 1, 5, 15, 30, 44, 46, 30, 1, 6, 21, 50, 89, 120, 120, 76, 1, 7, 28, 77, 160, 259, 329, 316, 196, 1, 8, 36, 112, 265, 496, 748, 904, 841, 512, 1, 9, 45, 156, 413, 873, 1509, 2148, 2493, 2257, 1535, 1, 10, 55, 210
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OFFSET

1,7


COMMENTS

For n >= 2, T(n,k)= number of nonneg.int. strings s(0),...,s(n) such that s(n)=nk, s(0)=s(1)=1, s(i)s(i1)<=1 for i >= 2.


LINKS

Table of n, a(n) for n=1..69.


FORMULA

T(n, k) = A026300(n, k)  A026300(n1, k1), T(1, 1) = 1.
T(i, 0)=1 for i >= 0, T(2, 1)=1, T(2, 2)=1, T(3, 1)=2, T(3, 2)=3, T(3, 3)=2; and for i >= 4, T(i, 1)=i1, T(i, i)=T(i1, i2)+T(i1, i1) and T(i, j)=T(i1, j2)+T(i1, j1)+T(i1, j) for j=2, 3, ...., i1.
Righthand columns have g.f. (1z)*M^k, where M is g.f. of Motzkin numbers (A001006).


EXAMPLE

1
1,1
1,1,1
1,2,3,2
1,3,6,7,5
1,4,10,16,18,12
1,5,15,30,44,46,30


CROSSREFS

Cf. Righthand columns include A002026, A026107, A026134, A026109, A026110. Row sums are in A025566. Central column is in A026112.
Sequence in context: A107357 A251718 A182457 * A060475 A168069 A231725
Adjacent sequences: A026102 A026103 A026104 * A026106 A026107 A026108


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling


EXTENSIONS

Edited by Ralf Stephan, Dec 18 2004


STATUS

approved



