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A131821
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Triangle read by rows: row n consists of n followed by (n-2) ones then n.
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14
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1, 2, 2, 3, 1, 3, 4, 1, 1, 4, 5, 1, 1, 1, 5, 6, 1, 1, 1, 1, 6, 7, 1, 1, 1, 1, 1, 7, 8, 1, 1, 1, 1, 1, 1, 8, 9, 1, 1, 1, 1, 1, 1, 1, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 14
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graph;
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n,1) = T(n,n) = n for n >= 1, and T(n,k) = 1 for 2 <= k <= n - 1, n >= 3.
G.f.: y*(x - 3*x^2*y^2 + (x^2 + x^3)*y^3)/((1 - y)^2*(1 - x*y)^2).
E.g.f.: (1 - x^2 +(x^2 + (x - x^2)*y)*exp(y) - (1 - (x - x^2)*y)*exp(x*y))/(1 - x). (End)
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EXAMPLE
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First few rows of the triangle are:
1;
2, 2;
3, 1, 3;
4, 1, 1, 4;
5, 1, 1, 1, 5;
6, 1, 1, 1, 1, 6;
7, 1, 1, 1, 1, 1, 7;
...
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MAPLE
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A131821 := proc(n, c) if c=1 or c=n then n ; else 1 ; fi ; end: for n from 1 to 16 do for c from 1 to n do printf("%d, ", A131821(n, c)) ; od: od: # R. J. Mathar, May 30 2008
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MATHEMATICA
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T[n_, k_] := If[k == 1 || k == n, n, 1];
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PROG
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(Maxima) T(n, k) := if k = 1 or k = n then n else 1$
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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