A096260 - OEIS

%I #15 Jun 13 2015 00:51:23

%S 1,3,9,25,62,205,534,2110,5844,25996,75592,359256,1080592,5314480,

%T 16315424,81638240,253481024,1279358656,3996074112,20256075136,

%U 63463817472,322392513280,1011648561664,5144661112320,16156254536704,82205698518016,258259323717632

%N 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.

%C 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

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,30,0,-280,0,960,0,-1024).

%F a(n) = A096227(n) + A097405(n) + 1

%F G.f.: -(1024*x^11+512*x^10+832*x^9+432*x^8-80*x^7-234*x^6-295*x^5-72*x^4+65*x^3+21*x^2-3*x-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)*(2*x^2-1)*(8*x^2-1)). [_Colin Barker_, Nov 23 2012]

%t 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 *)

%Y Cf. A096222.

%Y Cf. A096227 (triangles created), A097405 (rectangles created).

%K nonn,easy

%O 0,2

%A _Pierre CAMI_, Aug 01 2004

%E Corrected and extended by _T. D. Noe_, Aug 09 2004 and Aug 16 2004

%E More terms from _Colin Barker_, Nov 23 2012