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 A026105 Triangle T read by rows: differences of Motzkin triangle (A026300). 15
 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, 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, 1353, 1, 10, 55, 210, 614, 1442, 2795, 4530, 6150, 6898, 6103, 3610 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS For n >= 2, T(n,k)= number of nonnegative integer 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 Right-hand columns include A002026, A026107, A026134, A026109, A026110. Row sums are in A025566. Central column is in A026112. Sequence in context: A251718 A182457 A334715 * A303868 A060475 A168069 Adjacent sequences:  A026102 A026103 A026104 * A026106 A026107 A026108 KEYWORD nonn,tabl AUTHOR EXTENSIONS Edited by Ralf Stephan, Dec 18 2004 a(65) corrected and more terms from Sean A. Irvine, Sep 16 2019 Offset set to 0 by Alois P. Heinz, Sep 16 2019 STATUS approved

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Last modified January 20 06:36 EST 2022. Contains 350467 sequences. (Running on oeis4.)