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%I #16 Jul 03 2020 14:55:05
%S 1,0,1,0,1,1,0,0,2,1,0,1,1,3,1,0,1,2,3,4,1,0,0,4,4,6,5,1,0,1,2,9,8,10,
%T 6,1,0,1,3,9,17,15,15,7,1,0,0,6,9,24,30,26,21,8,1,0,1,3,18,26,51,51,
%U 42,28,9,1
%N Riordan array (1, x*(1+x)/(1-x^3)).
%C Triangle T(n,k), read by rows, given by (0, 1, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C Antidiagonals sums: see A159284.
%D A. Luzón, D. Merlini, M. A. Morón, R. Sprugnoli, Complementary Riordan arrays, Discrete Applied Mathematics, 172 (2014) 75-87.
%H Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
%F Sum_{k, 0<=k<=n} T(n,k) = A001590(n+2), n>0.
%F Sum_{k, 0<=k<=n}T(n,k)*(-1)^(n-k) = A078056(n-1), n>0.
%F T(n,n) = A000012(n), T(n+1,n) = A001477(n) = n, T(n+2,n) = A161680(n) = A000217(n-1); T(n+3,n) = A000125(n-1), n>=1.
%F G.f.: (-1+x)*(1+x+x^2)/(-1+x^3+x*y+x^2*y). - _R. J. Mathar_, Aug 11 2015
%e Triangle begins:
%e 1
%e 0, 1
%e 0, 1, 1
%e 0, 0, 2, 1
%e 0, 1, 1, 3, 1
%e 0, 1, 2, 3, 4, 1
%e 0, 0, 4, 4, 6, 5, 1
%e 0, 1, 2, 9, 8, 10, 6, 1
%e 0, 1, 3, 9, 17, 15, 15, 7, 1
%Y Cf. Columns: A000007, A011655, A186731, A185395, A185292.
%Y Cf. Diagonals: A000012, A001477, A161680, A000125.
%K nonn,tabl
%O 0,9
%A _Philippe Deléham_, Jan 26 2012
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