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A252817 Number of n X 5 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down. 1
11, 81, 468, 2078, 7564, 23664, 65711, 165685, 385736, 839799, 1726761, 3379640, 6336411, 11439478, 19972358, 33843927, 55832593, 89905021, 141626554, 218683266, 331538662, 494251420, 725484265, 1049738089, 1498849798 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/259200)*n^10 + (1/6480)*n^9 + (149/60480)*n^8 + (163/7560)*n^7 + (10411/86400)*n^6 + (209/432)*n^5 + (17977/12960)*n^4 + (6043/3240)*n^3 + (37673/12600)*n^2 + (1423/1260)*n + 3.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(11 - 40*x + 182*x^2 - 430*x^3 + 711*x^4 - 822*x^5 + 657*x^6 - 360*x^7 + 131*x^8 - 29*x^9 + 3*x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)
EXAMPLE
Some solutions for n=4:
..0..1..1..2..3....0..1..2..3..3....0..1..1..2..3....0..0..1..2..3
..1..2..2..3..3....1..2..2..3..4....1..1..2..3..4....1..1..2..3..4
..2..3..3..4..4....2..2..2..3..4....1..2..3..4..4....1..2..2..3..4
..2..3..4..5..5....2..2..3..4..5....2..3..3..4..5....1..2..3..4..5
CROSSREFS
Column 5 of A252820.
Sequence in context: A156847 A119364 A305826 * A210064 A323223 A211557
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 22 2014
STATUS
approved

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Last modified June 16 07:04 EDT 2024. Contains 373423 sequences. (Running on oeis4.)