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A252820 T(n,k)=Number of nXk 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 8
1, 2, 2, 4, 6, 4, 7, 17, 17, 7, 11, 40, 63, 40, 11, 16, 81, 187, 187, 81, 16, 22, 147, 468, 684, 468, 147, 22, 29, 246, 1032, 2078, 2078, 1032, 246, 29, 37, 387, 2067, 5490, 7564, 5490, 2067, 387, 37, 46, 580, 3840, 13015, 23664, 23664, 13015, 3840, 580, 46, 56, 836, 6716 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1...2.....4......7.....11......16.......22........29........37.........46
..2...6....17.....40.....81.....147......246.......387.......580........836
..4..17....63....187....468....1032.....2067......3840......6716......11179
..7..40...187....684...2078....5490....13015.....28299.....57338.....109549
.11..81...468...2078...7564...23664....65711....165685....385736.....839799
.16.147..1032...5490..23664...86724...279300....809349...2147638....5289321
.22.246..2067..13015..65711..279300..1033761...3414257..10248688...28359679
.29.387..3840..28299.165685..809349..3414257..12755742..43017980..132916561
.37.580..6716..57338.385736.2147638.10248688..43017980.161986236..555724696
.46.836.11179.109549.839799.5289321.28359679.132916561.555724696.2106102800
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = (1/2)*n^2 - (1/2)*n + 1
k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 - (1/24)*n^2 + (7/12)*n + 1
k=3: [polynomial of degree 6]
k=4: [polynomial of degree 8]
k=5: [polynomial of degree 10]
k=6: [polynomial of degree 12]
k=7: [polynomial of degree 14]
Empirical for "within 1" instead of "within 2" is T(n,k)=binomial(n+k,k)-1
EXAMPLE
Some solutions for n=4 k=4
..0..1..2..2....0..1..2..3....0..0..1..1....0..1..2..3....0..0..0..1
..1..1..2..3....1..1..2..3....0..1..2..2....1..2..3..3....0..1..1..2
..2..2..3..4....1..1..2..3....1..2..3..3....2..3..3..4....1..2..2..3
..2..3..4..5....1..2..3..4....1..2..3..4....2..3..4..4....2..2..3..4
CROSSREFS
Column 1 is A000124(n-1)
Sequence in context: A232065 A219741 A210603 * A218765 A219310 A220070
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 22 2014
STATUS
approved

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Last modified July 14 15:52 EDT 2024. Contains 374322 sequences. (Running on oeis4.)