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 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 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. LINKS 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). 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. Right-hand columns include A002026, A026107, A026134, A026109, A026110. Row sums are in A025566. Central column is in A026112. Sequence in context: A107357 A251718 A182457 * A303868 A060475 A168069 Adjacent sequences:  A026102 A026103 A026104 * A026106 A026107 A026108 KEYWORD nonn,tabl AUTHOR EXTENSIONS Edited by Ralf Stephan, Dec 18 2004 STATUS approved

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Last modified August 15 07:26 EDT 2018. Contains 313756 sequences. (Running on oeis4.)