

A096260


Number of different triangles, squares and rectangles created when a square piece of paper is folded n times, the first time by a diagonal of the square and after by the median of the triangle.


2



1, 3, 9, 25, 62, 205, 534, 2110, 5844, 25996, 75592, 359256, 1080592, 5314480, 16315424, 81638240, 253481024, 1279358656, 3996074112, 20256075136, 63463817472, 322392513280, 1011648561664, 5144661112320, 16156254536704, 82205698518016, 258259323717632
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

After unfolding the paper, the count consists of (a) triangles whose hypotenuse is parallel to the sides of the original square, (b) triangles whose hypotenuse is diagonal to the sides of the original square, (c) rectangles whose sides are parallel to the sides of the original square and (d) rectangles whose sides are diagonal to the sides of the original square. Note that the count for (c) is A096222(2*(Ceiling(n/2)1)). E.g. a(5) = 205 because the counts are a=32, b=64, c=100, d=9.  T. D. Noe, Aug 09 2004


LINKS



FORMULA

G.f.: (1024*x^11+512*x^10+832*x^9+432*x^880*x^7234*x^6295*x^572*x^4+65*x^3+21*x^23*x1) / ((2*x1)*(2*x+1)*(4*x1)*(4*x+1)*(2*x^21)*(8*x^21)). [Colin Barker, Nov 23 2012]


MATHEMATICA

Join[{1, 3, 9, 25}, LinearRecurrence[{0, 30, 0, 280, 0, 960, 0, 1024}, {62, 205, 534, 2110, 5844, 25996, 75592, 359256}, 20]] (* Harvey P. Dale, Apr 08 2015 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

Corrected and extended by T. D. Noe, Aug 09 2004 and Aug 16 2004


STATUS

approved



