Search: id:A059347
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%I A059347
%S A059347 1,0,1,1,1,2,0,1,2,4,2,2,3,5,9,0,2,4,7,12,21,5,5,7,11,18,30,51,0,5,10,
%T A059347 17,28,46,76,127,14,14,19,29,46,74,120,196,323,0,14,28,47,76,122,196,
%U A059347 316,512,835,42,42,56,84,131,207,329,525,841,1353,2188,0,42,84,140,224
%N A059347 Difference array of Motzkin numbers A001006 read by antidiagonals.
%C A059347 Row sums of odd rows (e.g. 4 = 1+1+2 for 3rd row) equal the Motzkin number 
               of next row. Row sums of even rows equal the Motzkin number of the 
               next row - n!/((n/2)!((n/2)+1)!) (i.e. A001006(n) - A000108(n/2) 
               where A000108 are the Catalan numbers). - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), 
               Dec 05 2004
%D A059347 F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 
               (1999) 73-112.
%e A059347 1; 0,1; 1,1,2; 0,1,2,4; ...
%Y A059347 Top row is A001006, leading diagonals give A000108 (interspersed with 
               0's), A000108 doubled up, A059348.
%Y A059347 Sequence in context: A166692 A046766 A003285 this_sequence A071496 A071502 
               A074704
%Y A059347 Adjacent sequences: A059344 A059345 A059346 this_sequence A059348 A059349 
               A059350
%K A059347 nonn,easy,nice,tabl
%O A059347 0,6
%A A059347 N. J. A. Sloane (njas(AT)research.att.com), Jan 27 2001
%E A059347 More terms from Larry Reeves (larryr(AT)acm.org), Feb 16 2001

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