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A026584
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Triangular array T read by rows: T(i,0)=T(i,2i)=1 for i >= 0, T(i,1)=T(i,2i-1)=[ i/2 ] for i >= 1 and for i >= 2 and 2<=j<=2i-2, T(i,j)=T(i-1,j-2)+T(i-1,j-1)+T(i-1,j) if i+j is odd, T(i,j)=T(i-1,j-2)+T(i-1,j) if i+j is even.
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20
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1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 4, 1, 1, 1, 2, 5, 7, 8, 7, 5, 2, 1, 1, 2, 8, 9, 20, 14, 20, 9, 8, 2, 1, 1, 3, 9, 19, 28, 43, 40, 43, 28, 19, 9, 3, 1, 1, 3, 13, 22, 56, 62, 111, 86, 111, 62, 56, 22, 13, 3, 1, 1, 4, 14, 38, 69, 140, 167, 259, 222, 259
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Row sums are in A026597. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2006
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FORMULA
| T(n, k) = number of integer strings s(0), ..., s(n) such that s(0)=0, s(n)=n-k, |s(i)-s(i-1)|<=1 if s(i-1) odd, |s(i)-s(i-1)|=1 if s(i-1) is even, for 1<=i<=n.
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EXAMPLE
| Triangle begins:
1;
1, 0, 1;
1, 1, 2, 1, 1;
1, 1, 4, 2, 4, 1, 1;
1, 2, 5, 7, 8, 7, 5, 2, 1;
1, 2, 8, 9, 20, 14, 20, 14, 9, 8, 2, 1;
1, 3, 9, 19, 28, 43, 40, 43, 28, 19, 9, 3, 1;
1, 3, 13, 22, 56, 62, 111, 86, 111, 62, 56, 22, 13, 3, 1;
1, 4, 14, 38, 69, 140, 167, 259, 222, 259, 167, 140, 69, 38, 14, 4, 1;
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CROSSREFS
| Sequence in context: A098120 A098873 A046876 * A174547 A119326 A146314
Adjacent sequences: A026581 A026582 A026583 * A026585 A026586 A026587
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KEYWORD
| nonn,tabf
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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