

A098921


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.


0



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
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OFFSET

1,2


COMMENTS

The vertices of these figures need not be in [n] X [n].


REFERENCES

Matthew Coppenbarger (Rochester Institute of Technology, Rochester, NY), Problem 11060 ("Little Boxes Made of TickyTacky"), American Mathematical Monthly, 111 (2004), 65; 113 (2005), 753754.


LINKS

Table of n, a(n) for n=1..33.
Index entries for linear recurrences with constant coefficients, signature (4,5,0,5,4,1).


FORMULA

F_n = (11n^42n^35n^222n+12)/12 for n even and F_n = (11n^42n^35n^222n+18)/12 for n odd. It can also be represented by the floor of the second expression for all n.
G.f.: x^2*(x^4+8*x^2+26*x+9) / ((x1)^5*(x+1)). [Colin Barker, Feb 18 2013]


MAPLE

F:= n > trunc((11*n^42*n^35*n^222*n+18)/12);


CROSSREFS

Sequence in context: A075139 A264376 A328955 * A027234 A081574 A084151
Adjacent sequences: A098918 A098919 A098920 * A098922 A098923 A098924


KEYWORD

nonn,easy


AUTHOR

Jerrold Grossman, Oct 17 2004


STATUS

approved



