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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

Table of n, a(n) for n=0..55.

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 February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)