

A086114


Number of 4 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.


3



8, 64, 216, 528, 1080, 1968, 3304, 5216, 7848, 11360, 15928, 21744, 29016, 37968, 48840, 61888, 77384, 95616, 116888, 141520, 169848, 202224, 239016, 280608, 327400, 379808, 438264, 503216, 575128, 654480, 741768, 837504, 942216, 1056448
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..34.
Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March challenge
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

a(n) = 2/3*n*(n^3+6*n^2+11*n6). More generally, number of m X n (0, 1) matrices such that each row and each column is increasing or decreasing is 2*n*(2*binomial(n+m1, n)m) = 4/Beta(m, n)2*m*n.
G.f.: 8*x*(x^33*x^2+3*x+1) / (x1)^5. [Colin Barker, Feb 22 2013]


CROSSREFS

Cf. A032260, A016742, A086113, A086115.
Sequence in context: A207393 A207940 A016743 * A209651 A207071 A117219
Adjacent sequences: A086111 A086112 A086113 * A086115 A086116 A086117


KEYWORD

nonn,easy


AUTHOR

Vladimir Baltic, Vladeta Jovovic, Jul 10 2003


STATUS

approved



