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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,30,-30,-280,280,960,-960,-1024,1024).
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))
G.f.: x^3*(256*x^7+880*x^6-360*x^5-706*x^4+113*x^3+149*x^2-9*x-8) / ((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]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, Aug 16 2004
STATUS
approved