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

0,2

Links

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

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)

Example

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

Crossrefs

Column 5 of A225010.

Sequence in context: A050256 A223835 A224143 * A352953 A070052 A203249

Adjacent sequences: A225004 A225005 A225006 * A225008 A225009 A225010

Keyword

nonn,easy

Author

R. H. Hardin, Apr 23 2013

Extensions

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

Status

approved