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 A122896 Riordan array for directed animals. 4
 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 5, 3, 1, 0, 9, 12, 9, 4, 1, 0, 21, 30, 25, 14, 5, 1, 0, 51, 76, 69, 44, 20, 6, 1, 0, 127, 196, 189, 133, 70, 27, 7, 1, 0, 323, 512, 518, 392, 230, 104, 35, 8, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Inverse of Riordan array (1, x/(1+x+x^2)). Product of A007318 and A122896 is A122897. Row sums are A005773, number of directed animals of size n. Riordan array (1, xm(x)) where m(x) is the g.f. of Motzkin numbers (A001006). - Philippe Deléham, Nov 04 2009 LINKS FORMULA Riordan array (1, (1-x-sqrt(1-2x-3x^2))/(2x)). T(n+1,k+1) = A064189(n,k). - Philippe Deléham, Apr 21 2007 EXAMPLE Triangle begins: 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 5, 3, 1, 0, 9, 12, 9, 4, 1, 0, 21, 30, 25, 14, 5, 1, 0, 51, 76, 69, 44, 20, 6, 1, 0, 127, 196, 189, 133, 70, 27, 7, 1, 0, 323, 512, 518, 392, 230, 104, 35, 8, 1, 0, 835, 1353, 1422, 1140, 726, 369, 147, 44, 9, 1 MAPLE T := proc(n, k) option remember; if k=0 then return 0^n fi; if k>n then return 0 fi; T(n-1, k-1) + T(n-1, k) + T(n-1, k+1) end: for n from 0 to 9 do seq(T(n, k), k=0..n) od; # Peter Luschny, Aug 17 2016 PROG (Sage) # Function riordan_array defined in A256893. riordan_array(1, (1-x-sqrt(1-2*x-3*x^2))/(2*x), 11) # Peter Luschny, Aug 17 2016 CROSSREFS Cf. A001006, A007318, A064189, A122897. Sequence in context: A216344 A229762 A062110 * A191348 A198792 A196182 Adjacent sequences:  A122893 A122894 A122895 * A122897 A122898 A122899 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Sep 18 2006 STATUS approved

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Last modified October 23 17:20 EDT 2018. Contains 316529 sequences. (Running on oeis4.)