A225007 Number of n X 5 0..1 arrays with rows unimodal and columns nondecreasing.

1, 16, 86, 296, 791, 1792, 3612, 6672, 11517, 18832, 29458, 44408, 64883, 92288, 128248, 174624, 233529, 307344, 398734, 510664, 646415, 809600, 1004180, 1234480, 1505205, 1821456, 2188746, 2613016, 3100651, 3658496, 4293872, 5014592, 5828977

Offset: 0

Author

R. H. Hardin, Apr 23 2013

Keywords

• nonn
• easy

Examples

			Some solutions for n=3:
  0 0 0 0 0    0 0 1 0 0    0 0 1 1 1    0 0 1 1 0
  0 0 0 1 0    0 1 1 0 0    0 0 1 1 1    0 0 1 1 1
  0 0 1 1 0    0 1 1 1 0    0 0 1 1 1    0 1 1 1 1
6*a(7) = 40032 = 1*6 + 6*15 + 15*28 + 28*45 + 45*66 + 66*91 + 91*120 + 120*153. - _Bruno Berselli_, Feb 05 2014
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000 (terms 1..210 from R. H. Hardin)

Crossrefs

Column 5 of A225010.

Formula

a(n) = (2/15)*n^5 + (7/6)*n^4 + (23/6)*n^3 + (35/6)*n^2 + (121/30)*n + 1.

6*a(n) = Sum_{i=1..n+1} A000384(i)*A000384(i+1). - Bruno Berselli, Feb 05 2014

From Colin Barker, Mar 16 2018: (Start)

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n >= 6.

G.f.: (1 + 10*x + 5*x^2) / (1 - x)^6. (End)

Extensions

a(0)=1 prepended by Andrew Howroyd, Feb 11 2024