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A101037
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Triangle read by rows: T(n,1) = T(n,n) = n and for 1<k<n: T(n,k) = floor((T(n-1,k-1)+T(n-1,k))/2).
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2
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1, 2, 2, 3, 2, 3, 4, 2, 2, 4, 5, 3, 2, 3, 5, 6, 4, 2, 2, 4, 6, 7, 5, 3, 2, 3, 5, 7, 8, 6, 4, 2, 2, 4, 6, 8, 9, 7, 5, 3, 2, 3, 5, 7, 9, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 11, 9, 7, 5, 3, 2, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 12, 13, 11, 9, 7, 5, 3, 2, 3, 5, 7, 9, 11, 13, 14, 12, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 12, 14
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OFFSET
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1,2
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COMMENTS
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For n>1: sum of n-th row = A007590(n+1).
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LINKS
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FORMULA
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T(n,k) = n - 2*k + 2 if k < (n+1)/2.
T(n,(n+1)/2) = 2 if n>1 is odd.
T(n,k) = 2*k - n if k > (n+1)/2.
G.f. as triangle: x*y*(x^6*y^3-2*x^5*y^3-2*x^5*y^2+x^4*y^3+3*x^4*y^2+x^4*y-3*x^2*y+1)/((1-x^2*y)*(1-x)^2*(1-x*y)^2)).
(End)
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EXAMPLE
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Triangle begins:
1;
2, 2;
3, 2, 3;
4, 2, 2, 4;
5, 3, 2, 3, 5;
6, 4, 2, 2, 4, 6;
7, 5, 3, 2, 3, 5, 7;
...
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MAPLE
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T:= proc(n, k) if k < (n+1)/2 then n-2*k+2 elif k=(n+1)/2 then 2 else 2*k-n fi end proc:
T(1, 1):= 1:
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MATHEMATICA
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T[n_, 1] := n; T[n_, n_] := n; T[n_, k_] := T[n, k] = Which[k < (n + 1)/2, n - 2*k + 2, k == (n + 1)/2, 2, True, 2*k - n];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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