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Search: id:A098921
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| A098921 |
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Let [n] = {1,2,...,n}. Let G_n be the union of all closed line segments joining any two elements of [n] X [n] along a vertical or horizontal line, or along a line with slope +-1. Then a(n) = combined total of the number of (nondegenerate) triangles and rectangles for which all edges are subsets of G_n. |
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+0
1
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| 0, 9, 62, 211, 534, 1127, 2112, 3629, 5844, 8941, 13130, 18639, 25722, 34651, 45724, 59257, 75592, 95089, 118134, 145131, 176510, 212719, 254232, 301541, 355164, 415637, 483522, 559399, 643874, 737571, 841140, 955249, 1080592
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The vertices of these figures need not be in [n] X [n].
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REFERENCES
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Matthew Coppenbarger (Rochester Institute of Technology, Rochester, NY), Problem 11060 ("Little Boxes Made of Ticky-Tacky"), American Mathematical Monthly, 111 (2004), 65; 113 (2005), 753-754.
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FORMULA
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F_n = (11n^4-2n^3-5n^2-22n+12)/12 for n even, and F_n = (11n^4-2n^3-5n^2-22n+18)/12 for n odd. It can also be represented by the floor of the second expression for all n.
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MAPLE
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F:= n -> trunc((11*n^4-2*n^3-5*n^2-22*n+18)/12);
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CROSSREFS
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Sequence in context: A126504 A025014 A075139 this_sequence A027234 A081574 A084151
Adjacent sequences: A098918 A098919 A098920 this_sequence A098922 A098923 A098924
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KEYWORD
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nonn
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AUTHOR
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Jerrold W. Grossman (grossman(AT)oakland.edu), Oct 17 2004
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