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A064580
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Triangle associated with rooted trees with a degree constraint (A036765).
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6
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1, 1, 1, 1, 2, 2, 1, 3, 5, 5, 1, 4, 9, 14, 13, 1, 5, 14, 28, 40, 36, 1, 6, 20, 48, 87, 118, 104, 1, 7, 27, 75, 161, 273, 357, 309, 1, 8, 35, 110, 270, 536, 866, 1100, 939, 1, 9, 44, 154, 423, 951, 1782, 2772, 3441, 2905, 1, 10, 54, 208, 630, 1572, 3310, 5928, 8946, 10900
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 21 2009: (Start)
Row sums = A161898: (1, 2, 5, 14, 41, 124, 384,...).
Right border = A136751.
Reversal of the triangle = a convergent of infinite products a*b*c,...
of "aerate and multiply" where a = A007318, b = A007318 interleaved with zeros
(by columns), c = A007318 interleaved with two adjacent zeros, and so on. (End)
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FORMULA
| a(n, k)=a(n-1, k)+a(n-1, k-1)+a(n-1, k-2)+a(n-1, k-3) with a(0, 0)=1 and a(n, k)=0 if n<k or k<0.
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CROSSREFS
| Columns include A000012, A000027, A000096. Right hand column is A036765. The sequence of triangles A010054 (Triangle Indicator), A007318 (Pascal), A026300 (Motzkin), A064580, ... converges to the triangle A009766 (Catalan).
A161898, A136751 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 21 2009]
Sequence in context: A139687 A188181 A064581 * A009766 A059718 A076038
Adjacent sequences: A064577 A064578 A064579 * A064581 A064582 A064583
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Sep 21 2001
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggsetion of Andrew Plewe, Jun 17 2007
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