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A026105
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Triangle T read by rows: differences of Motzkin triangle (A026300).
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15
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| For n >= 2, T(n,k)= number of nonneg.int. strings s(0),...,s(n) such that s(n)=n-k, s(0)=s(1)=1, |s(i)-s(i-1)|<=1 for i >= 2.
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FORMULA
| T(n, k) = A026300(n, k) - A026300(n-1, k-1), 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)=i-1, T(i, i)=T(i-1, i-2)+T(i-1, i-1) and T(i, j)=T(i-1, j-2)+T(i-1, j-1)+T(i-1, j) for j=2, 3, ...., i-1.
Right-hand columns have g.f. (1-z)*M^k, where M is g.f. of Motzkin numbers (A001006).
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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
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CROSSREFS
| Cf. Right-hand columns include A002026, A026107, A026134, A026109, A026110. Row sums are in A025566. Central column is in A026112.
Sequence in context: A037222 A102288 A107357 * A060475 A168069 A106559
Adjacent sequences: A026102 A026103 A026104 * A026106 A026107 A026108
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Edited by Ralf Stephan, Dec 18 2004
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