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 A112743 An aerated Delannoy triangle. 0
 1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 1, 0, 5, 0, 1, 0, 5, 0, 7, 0, 1, 1, 0, 13, 0, 9, 0, 1, 0, 7, 0, 25, 0, 11, 0, 1, 1, 0, 25, 0, 41, 0, 13, 0, 1, 0, 9, 0, 63, 0, 61, 0, 15, 0, 1, 1, 0, 41, 0, 129, 0, 85, 0, 17, 0, 1, 0, 11, 0, 129, 0, 231, 0, 113, 0, 19, 0, 1, 1, 0, 61, 0, 321, 0, 377, 0, 145, 0, 21, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are tribonacci numbers A000073. Diagonal sums are aerated Pell numbers. LINKS FORMULA Riordan array (1/(1-x^2), x(1+x^2)/(1-x^2)). Number triangle T(n,k) = if(k<=n, Sum_{j=0..k} (1+(-1)^(n-k))binomial(k,j)binomial((n-k)/2,j)2^j/2, 0). T(n,k) = T(n-1,k-1) + T(n-2,k) + T(n-3,k-1). - Philippe Deléham, Mar 11 2013 EXAMPLE Rows begin   1;   0,  1;   1,  0,  1;   0,  3,  0,  1;   1,  0,  5,  0,  1;   0,  5,  0,  7,  0,  1;   1,  0, 13,  0,  9,  0,  1;   0,  7,  0, 25,  0, 11,  0,  1;   1,  0, 25,  0, 41,  0, 13,  0,  1; CROSSREFS Cf. A008288, A114123, A216182. Sequence in context: A317595 A263753 A303877 * A230427 A229995 A119467 Adjacent sequences:  A112740 A112741 A112742 * A112744 A112745 A112746 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Sep 17 2005 STATUS approved

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Last modified May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)