login
A340228
a(n) is the sum of the lengths of all the segments used to draw a rectangle of height 2^(n-1) and width n divided into 2^(n-1) rectangles of unit height, in turn, divided into rectangles of unit height and lengths corresponding to the parts of the compositions of n.
0
4, 11, 27, 64, 149, 342, 775, 1736, 3849, 8458, 18443, 39948, 86029, 184334, 393231, 835600, 1769489, 3735570, 7864339, 16515092, 34603029, 72351766, 150994967, 314572824, 654311449, 1358954522, 2818572315, 5838471196, 12079595549, 24964497438, 51539607583, 106300440608
OFFSET
1,1
FORMULA
O.g.f.: x*(4 - 13*x + 13*x^2 - 3*x^3)/(1 - 3*x + 2*x^2)^2.
E.g.f.: (exp(2*x)*(3 + 6*x) + 4*x*exp(x) - 3)/4.
a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 4.
a(n) = n + 3*(n + 1)*2^(n-2).
a(n) = A001792(n) + A188626(n).
a(n) = A045623(n) + A215149(n).
a(n) = A006127(n) + A053220(n).
EXAMPLE
Illustrations for n = 1..4:
_ _ _
|_| |_ _|
|_|_|
a(1) = 4 a(2) = 11
_ _ _ _ _ _ _
|_ _ _| |_ _ _ _|
|_ _|_| |_ _ _|_|
|_|_ _| |_|_ _ _|
|_|_|_| |_ _|_ _|
|_ _|_|_|
|_|_ _|_|
|_|_|_ _|
|_|_|_|_|
a(3) = 27 a(4) = 64
MATHEMATICA
LinearRecurrence[{6, -13, 12, -4}, {4, 11, 27, 64}, 32]
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Jan 01 2021
STATUS
approved