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Search: id:A097472
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| A097472 |
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Number of different candle trees having a total of m edges. |
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+0
1
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| 1, 3, 10, 31, 96, 296, 912, 2809, 8651, 26642, 82047, 252672, 778128, 2396320, 7379697, 22726483, 69988378, 215535903, 663763424, 2044122936, 6295072048, 19386276329, 59701891739, 183857684514, 566207320575, 1743689586432
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A candle tree is a graph on the plane square lattice Z X Z whose edges have length one with the following properties: (a) It contains a line segment ("trunk") of length from 0 to m on the vertical axis, its lowest node is at the origin. (b) It contains horizontal line segments ("branches"); each of them intersects the trunk. (c) Each branch is allowed to have "candles", which are vertical edges of length 1, whose lower node is on a branch.
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REFERENCES
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Alexander Malkis, "Polyedges, polyominoes and the 'Digit' game", diploma thesis in computer science, Universitaet des Saarlandes, Germany
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LINKS
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Alexander Malkis, Polyedges, polyominoes and the 'Digit' game
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FORMULA
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a(n) = sum_{s, d, k>=0 with s+d+k=m} binom(s+2d+1, s)*binom(s, k); generating function = 1/(x^4 + 2x^3 - x^2 - 3x + 1); a(n+4) = 3a(n+3)+a(n+2)-2a(n+1)-a(n)
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CROSSREFS
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Bisection of A060945 and |A077930|.
Sequence in context: A033121 A106517 A055217 this_sequence A068094 A100058 A002160
Adjacent sequences: A097469 A097470 A097471 this_sequence A097473 A097474 A097475
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Alexander Malkis (alexmalk(AT)studcs.uni-sb.de), Sep 18 2004
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