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Search: id:A026568
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| A026568 |
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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+1)/2 ] for i >= 1 and for i >= 2 and 2<=j<=i-2, T(i,j)=T(i-1,j-2)+T(i-1,j-1)+T(i-1,j) if i+j is even, T(i,j)=T(i-1,j-2)+T(i-1,j) if i+j is odd. |
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+0
22
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| 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 4, 5, 4, 2, 1, 1, 2, 7, 7, 13, 7, 7, 2, 1, 1, 3, 8, 16, 20, 27, 20, 16, 8, 3, 1, 1, 3, 12, 19, 44, 43, 67, 43, 44, 19, 12, 3, 1, 1, 4, 13, 34, 56, 106, 111, 153, 111, 106, 56, 34, 13, 4, 1, 1, 4, 18, 38, 103, 140, 273
(list; table; graph; listen)
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OFFSET
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1,7
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FORMULA
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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) is even, |s(i)-s(i-1)|=1 if s(i-1) is odd, for 1<=i<=n.
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PROGRAM
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(PARI) T(k, n)=if(n<0||n>2*k, 0, if(n==0||n==2*k, 1, if(k>0&&(n==1||n==2*k-1), (k+1)\2, T(k-1, n-2)+T(k-1, n)+if((k+n)%2==0, T(k-1, n-1))))) (from R. Stephan)
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CROSSREFS
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Adjacent sequences: A026565 A026566 A026567 this_sequence A026569 A026570 A026571
Sequence in context: A132409 A030337 A136406 this_sequence A138361 A030408 A068153
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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