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A225007 Number of n X 5 0..1 arrays with rows unimodal and columns nondecreasing. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 5 of A225010.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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( A000384(i)*A000384(i+1), i=1..n+1 ), which is satisfied even starting from a(0)=1. - Bruno Berselli, Feb 05 2014

From Colin Barker, Mar 16 2018: (Start)

G.f.: x*(16 - 10*x + 20*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.

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.

(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

Cf. A225010.

Sequence in context: A050256 A223835 A224143 * A070052 A203249 A022676

Adjacent sequences:  A225004 A225005 A225006 * A225008 A225009 A225010

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin, Apr 23 2013

STATUS

approved

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)