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A223954 Number of 7 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing. 1
128, 2187, 6869, 12856, 20275, 31899, 52532, 89135, 152495, 259230, 434069, 712692, 1145194, 1800237, 2769954, 4175669, 6174497, 8966888, 12805179, 18003218, 24947124, 34107247, 46051392, 61459371, 81138947, 106043234, 137289617 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 7 of A223949.
LINKS
FORMULA
Empirical: a(n) = (4/315)*n^7 - (1/45)*n^6 + (34/45)*n^5 + (221/72)*n^4 + (4507/180)*n^3 + (42283/360)*n^2 + (53997/140)*n + 7577 for n>5.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(128 + 1163*x - 7043*x^2 + 11972*x^3 - 3753*x^4 - 9075*x^5 + 7046*x^6 + 2119*x^7 - 1755*x^8 - 2009*x^9 + 1146*x^10 + 346*x^11 - 221*x^12) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..0....1..1..1....1..1..1....0..1..1....0..0..1....0..1..1....0..1..1
..1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..1..1....1..1..1
..0..0..1....0..0..1....0..0..0....0..0..0....0..0..1....1..1..1....0..1..1
..0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....0..1..1....0..0..0
..0..0..1....0..1..1....0..1..1....0..0..1....0..0..0....1..1..1....0..0..0
..1..1..1....0..0..0....0..0..1....1..1..1....0..1..1....0..1..1....0..0..1
..0..1..1....0..1..1....0..0..1....0..0..1....0..0..0....0..0..1....0..1..1
CROSSREFS
Cf. A223949.
Sequence in context: A195594 A321831 A351195 * A224138 A331198 A250365
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 29 2013
STATUS
approved

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Last modified March 3 09:53 EST 2024. Contains 370510 sequences. (Running on oeis4.)