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 A165408 An aerated Catalan array. 3
 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 2, 0, 4, 0, 1, 0, 0, 0, 5, 0, 5, 0, 1, 0, 0, 0, 0, 9, 0, 6, 0, 1, 0, 0, 0, 5, 0, 14, 0, 7, 0, 1, 0, 0, 0, 0, 14, 0, 20, 0, 8, 0, 1, 0, 0, 0, 0, 0, 28, 0, 27, 0, 9, 0, 1, 0, 0, 0, 0, 14, 0, 48, 0, 35, 0, 10, 0, 1, 0, 0, 0, 0, 0, 42, 0, 75, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Aeration of A120730. Row sums are A165407. LINKS FORMULA Number triangle T(n,k)=if(n<=3k, C((n+k)/2,k)*((3k-n)/2+1)*(1+(-1)^(n-k))/(2(k+1)),0); G.f.: 1/(1-xy-x^3y/(1-x^3y/(1-x^3y/(1-x^3y/(1-... (continued fraction). EXAMPLE Triangle begins 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 2, 0, 4, 0, 1, 0, 0, 0, 5, 0, 5, 0, 1, 0, 0, 0, 0, 9, 0, 6, 0, 1, 0, 0, 0, 5, 0, 14, 0, 7, 0, 1, 0, 0, 0, 0, 14, 0, 20, 0, 8, 0, 1, 0, 0, 0, 0, 0, 28, 0, 27, 0, 9, 0, 1, 0, 0, 0, 0, 14, 0, 48, 0, 35, 0, 10, 0, 1 CROSSREFS Sequence in context: A187144 A123635 A124304 * A186733 A171368 A322353 Adjacent sequences:  A165405 A165406 A165407 * A165409 A165410 A165411 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Sep 17 2009 STATUS approved

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Last modified October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)