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A219350 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array. 1
4, 4, 15, 35, 81, 174, 364, 740, 1459, 2778, 5105, 9069, 15615, 26129, 42600, 67827, 105680, 161425, 242124, 357122, 518634, 742446, 1048745, 1463094, 2017569, 2752076, 3715867, 4969275, 6585689, 8653791, 11280078, 14591693, 18739590 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 4 of A219354.
LINKS
FORMULA
Empirical: a(n) = (1/40320)*n^8 - (1/1120)*n^7 + (5/192)*n^6 - (2/5)*n^5 + (7429/1920)*n^4 - (3037/160)*n^3 + (34483/2016)*n^2 + (71507/280)*n - 791 for n>7.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(4 - 32*x + 123*x^2 - 292*x^3 + 474*x^4 - 555*x^5 + 496*x^6 - 364*x^7 + 235*x^8 - 139*x^9 + 82*x^10 - 48*x^11 + 22*x^12 - 7*x^13 + 3*x^14 - x^15) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>16.
(End)
EXAMPLE
Some solutions for n=3:
..0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1....1..1..1..1
..0..0..0..1....0..0..0..1....0..0..0..0....0..0..1..1....1..1..1..1
..0..0..0..1....0..0..0..1....0..0..0..0....1..1..1..1....1..1..1..1
CROSSREFS
Cf. A219354.
Sequence in context: A048282 A068592 A198313 * A222511 A135944 A268169
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 18 2012
STATUS
approved

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Last modified June 25 04:03 EDT 2024. Contains 373697 sequences. (Running on oeis4.)