login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 Ticky-Tacky"), American Mathematical Monthly, 111 (2004), 65; 113 (2005), 753-754.

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^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.

G.f.: -x^2*(x^4+8*x^2+26*x+9) / ((x-1)^5*(x+1)). [Colin Barker, Feb 18 2013]

MAPLE

F:= n -> trunc((11*n^4-2*n^3-5*n^2-22*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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 21 01:23 EST 2019. Contains 329348 sequences. (Running on oeis4.)