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A086115 Number of 5 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing. 4
10, 100, 390, 1080, 2470, 4980, 9170, 15760, 25650, 39940, 59950, 87240, 123630, 171220, 232410, 309920, 406810, 526500, 672790, 849880, 1062390, 1315380, 1614370, 1965360, 2374850, 2849860, 3397950, 4027240, 4746430, 5564820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..30.

Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March challenge

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = 1/6*n*(n^4+10*n^3+35*n^2+50*n-36). 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.: -10*x*(x^4-4*x^3+6*x^2-4*x-1) / (x-1)^6. [Colin Barker, Feb 22 2013]

CROSSREFS

Cf. A032260, A016742, A086113, A086114.

Sequence in context: A208024 A207804 A060522 * A209652 A207072 A207405

Adjacent sequences:  A086112 A086113 A086114 * A086116 A086117 A086118

KEYWORD

nonn,easy

AUTHOR

Vladimir Baltic, Vladeta Jovovic, Jul 10 2003

STATUS

approved

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Last modified February 24 07:30 EST 2018. Contains 299597 sequences. (Running on oeis4.)