|
| |
|
|
A097405
|
|
Number of different rectangles created when a square sheet of paper is folded n times, the first time by one of the diagonals of the square and after by the median of the triangle.
|
|
1
| |
|
|
0, 0, 8, 17, 108, 265, 1461, 4011, 21211, 62135, 322423, 977647, 5025263, 15510495, 79345631, 247115711, 1261100991, 3945447295, 20110344063, 63059984127, 321227980543, 1008422616575, 5135350103551, 16130465856511, 82131231439871
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| There are two types of rectangles: (1) those whose edges are parallel to the edges of the initial square and (2) those whose edges are diagonal to the edges of the initial square. These rectangles are enumerated by the p(x) and d(x) functions.
|
|
|
FORMULA
| Let p(x) = x^2 (x+1)^2/4 and d(x) = (x^4 - x^2 - 6 x)/24. Then, for n>1, a(n) = -1 + p(2^ceiling(n/2-1)) + d(2^floor(n/2))
|
|
|
CROSSREFS
| Cf. A096260, A096227, A096531.
Sequence in context: A134790 A177129 A177178 * A192282 A088588 A041537
Adjacent sequences: A097402 A097403 A097404 * A097406 A097407 A097408
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Aug 16 2004
|
| |
|
|
