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Search: id:A030111
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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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+0
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, 26, 70
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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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 (pbarry(AT)wit.ie), Sep 30 2006
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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, C([ (n+k)/2 ], k)) = F(n+2)-1 where F(n) is the n-th Fibonacci number - Benoit Cloitre (benoit7848c(AT)orange.fr), 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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PROGRAM
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(PARI) T(n, k)=C((n+k)\2, k) where C(n, k)=if(k<0|k>n, 0, n!/k!/(n-k)!)
(PARI) printp(matrix(8, 8, n, k, C((n+k)\2, k)))
(PARI) for(n=1, 7, for(k=1, n, print1(C((n+k)\2, k)); if(k==n, print1("; ")); print1(" ")))
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CROSSREFS
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Cf. A066170.
Adjacent sequences: A030108 A030109 A030110 this_sequence A030112 A030113 A030114
Sequence in context: A117935 A103462 A116855 this_sequence A096921 A037161 A133255
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KEYWORD
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tabl,nonn
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AUTHOR
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Jacques Haubrich (jhaubrich(AT)freeler.nl)
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EXTENSIONS
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Description corrected by Michael Somos
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