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A030111
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Triangular array in which k-th entry in n-th row is C([ (n+k)/2 ],k) (1<=k<=n).
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4
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1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 3, 4, 1, 1, 3, 6, 4, 5, 1, 1, 4, 6, 10, 5, 6, 1, 1, 4, 10, 10, 15, 6, 7, 1, 1, 5, 10, 20, 15, 21, 7, 8, 1, 1, 5, 15, 20, 35, 21, 28, 8, 9, 1, 1, 6, 15, 35, 35, 56, 28, 36, 9, 10, 1, 1, 6, 21, 35, 70, 56, 84, 36, 45, 10, 11, 1, 1, 7, 21, 56, 70, 126, 84, 120, 45, 55, 11, 12, 1
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OFFSET
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1,4
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COMMENTS
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Same as A046854, but missing the initial column of ones.
Riordan array (1/((1-x)(1-x^2)),x/(1-x^2)). Diagonal sums are A052551. - Paul Barry, Sep 30 2006
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LINKS
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FORMULA
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G.f.: 1 / (1 - x - xy - x^2 + x^2y + x^3). - Ralf Stephan, Feb 13 2005
Sum(k=1, n, T(n, k)) = F(n+2)-1 where F(n) is the n-th Fibonacci number. - Benoit Cloitre, Oct 07 2002
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EXAMPLE
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1;
1 1;
2 1 1;
2 3 1 1;
3 3 4 1 1;
3 6 4 5 1 1;
...
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MATHEMATICA
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Flatten[Table[Binomial[Floor[(n+k)/2], k], {n, 20}, {k, n}]] (* Harvey P. Dale, Jun 03 2014 *)
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PROG
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(PARI) {T(n, k) = binomial((n+k)\2, k)}; /* Michael Somos, Jul 23 1999 */
(PARI) printp(matrix(8, 8, n, k, binomial((n+k)\2, k)))
(PARI) for(n=1, 7, for(k=1, n, print1(binomial((n+k)\2, k)); if(k==n, print1("; ")); print1(" ")))
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CROSSREFS
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KEYWORD
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AUTHOR
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Jacques Haubrich (jhaubrich(AT)freeler.nl)
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EXTENSIONS
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STATUS
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approved
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