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Search: id:A115990
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| A115990 |
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Riordan array (1/sqrt(1-2x-3x^2),((1-2x-3x^2)/(2(1-3x))-sqrt(1-2x-3x^2)/2). |
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+0
1
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| 1, 1, 1, 3, 2, 1, 7, 5, 3, 1, 19, 13, 8, 4, 1, 51, 35, 22, 12, 5, 1, 141, 96, 61, 35, 17, 6, 1, 393, 267, 171, 101, 53, 23, 7, 1, 1107, 750, 483, 291, 160, 77, 30, 8, 1, 3139, 2123, 1373, 839, 476, 244, 108, 38, 9, 1, 8953, 6046, 3923, 2423, 1406, 752, 360, 147, 47, 10
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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First column is central trinomial coefficients A002426. Second column is number of directed animals of size n+1, A005773(n+1). Row sums are A005717 (number of horizontal steps in all Motzkin paths of length n). First column has e.g.f. exp(x) I_0(2x). Row sums have e.g.f. dif(exp(x) I_1(2x),x).
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FORMULA
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Number triangle T(n,k)=sum{j=0..n, C(n-k,j-k)C(j,n-j)}.
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EXAMPLE
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Triangle begins
1,
1, 1,
3, 2, 1,
7, 5, 3, 1,
19, 13, 8, 4, 1,
51, 35, 22, 12, 5, 1,
141, 96, 61, 35, 17, 6, 1
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CROSSREFS
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Sequence in context: A001355 A105531 A129689 this_sequence A094531 A111960 A130462
Adjacent sequences: A115987 A115988 A115989 this_sequence A115991 A115992 A115993
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 10 2006
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