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A108914 Number of regions formed inside square by diagonals and the segments joining the vertices to the points dividing the sides into n equal length segments. 3
4, 32, 96, 188, 332, 460, 712, 916, 1204, 1488, 1904, 2108, 2716, 3080, 3532, 4068, 4772, 5140, 6016, 6392, 7188, 7992, 8932, 9260, 10484, 11312, 12208, 12968, 14396, 14660, 16504, 17220, 18346, 19680, 20756, 21548, 23692, 24728, 25992, 26868 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..40.

L. Smiley, The case n=6. Note 3- and 4-fold off-diagonal concurrencies

L. Smiley, The case n=7. Note there are no off-diagonal concurrencies

FORMULA

If n=1 or n is prime, a(n)=18*n^2-26*n+12.

If n is composite, vanishing regions from 3- and 4-fold concurrency must be subtracted.

CROSSREFS

A092098 is the corresponding count for triangles.

Sequence in context: A012036 A153794 A222326 * A052469 A211625 A211630

Adjacent sequences:  A108911 A108912 A108913 * A108915 A108916 A108917

KEYWORD

nonn

AUTHOR

Len Smiley and Brian Wick ( mathclub(AT)math.uaa.alaska.edu ), Jul 19 2005

STATUS

approved

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Last modified December 7 17:41 EST 2019. Contains 329847 sequences. (Running on oeis4.)