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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 (list; graph; refs; listen; history; text; internal format)
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*n-6). 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+m-1, n)-m) = 4/Beta(m, n)-2*m*n.

G.f.: -8*x*(x^3-3*x^2+3*x+1) / (x-1)^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

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)