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 A278676 T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake. 8

%I #4 Nov 25 2016 15:21:58

%S 0,1,1,4,8,4,10,33,33,10,20,99,158,99,20,35,245,579,579,245,35,56,532,

%T 1801,2650,1801,532,56,84,1050,4999,10584,10584,4999,1050,84,120,1926,

%U 12727,38848,55854,38848,12727,1926,120,165,3333,30218,134265,280616

%N T(n,k)=Number of nXk 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

%C Table starts

%C ...0....1......4......10........20.........35...........56.............84

%C ...1....8.....33......99.......245........532.........1050...........1926

%C ...4...33....158.....579......1801.......4999........12727..........30218

%C ..10...99....579....2650.....10584......38848.......134265.........441349

%C ..20..245...1801...10584.....55854.....280616......1378241........6654535

%C ..35..532...4999...38848....280616....1998526.....14437336......106388729

%C ..56.1050..12727..134265...1378241...14437336....157706284.....1809189550

%C ..84.1926..30218..441349...6654535..106388729...1809189550....32788533228

%C .120.3333..67651.1384443..31404174..791018703..21622163723...632621335872

%C .165.5500.143936.4148373.143558071.5827280865.263667893290.12823358704308

%H R. H. Hardin, <a href="/A278676/b278676.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

%F k=1: a(n) = (1/6)*n^3 - (1/6)*n

%F k=2: [polynomial of degree 6]

%F k=3: [polynomial of degree 11]

%F k=4: [polynomial of degree 20]

%F k=5: [polynomial of degree 37]

%F k=6: [polynomial of degree 70]

%e Some solutions for n=4 k=4

%e ..0..0..1..0. .0..1..0..0. .1..1..0..0. .0..0..1..0. .0..0..0..0

%e ..1..0..1..1. .0..1..1..0. .0..0..0..0. .1..1..0..0. .0..1..1..0

%e ..1..1..0..1. .1..0..0..1. .0..0..1..0. .1..1..1..0. .0..1..1..1

%e ..1..1..1..1. .1..0..1..1. .1..0..1..1. .1..1..1..1. .1..1..1..0

%Y Column 1 is A000292(n-1).

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Nov 25 2016

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Last modified June 24 02:53 EDT 2024. Contains 373661 sequences. (Running on oeis4.)