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A215182 T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value 12
2, 3, 2, 4, 4, 2, 5, 6, 5, 2, 6, 9, 12, 9, 2, 7, 12, 22, 26, 17, 2, 8, 16, 38, 83, 80, 48, 2, 9, 20, 64, 192, 412, 328, 141, 2, 10, 25, 98, 445, 1558, 3216, 1584, 559, 2, 11, 30, 145, 892, 5096, 18940, 36645, 9026, 2231, 2, 12, 36, 210, 1752, 14826, 102958, 364970, 635051 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.2..3..4...5....6....7.....8.....9....10.....11.....12.....13......14......15

.2..4..6...9...12...16....20....25....30.....36.....42.....49......56......64

.2..5.12..22...38...64....98...145...210....291....394....526.....684.....876

.2..9.26..83..192..445...892..1752..3136...5494...9074..14716...22842...34868

.2.17.80.412.1558.5096.14826.39630.97184.223612.482160.991120.1946560.3679402

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..607

FORMULA

Empirical for row n:

n=1: a(k)=2*a(k-1)-a(k-2)

n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4)

n=3: a(k)=2*a(k-1)-3*a(k-4)+3*a(k-6)-2*a(k-9)+a(k-10)

n=4: (order 39 symmetric)

EXAMPLE

Some solutions for n=4 k=4

.....3........2........1........3........2........3........3........2

....2.4......1.3......0.2......2.4......1.3......2.4......3.3......2.2

...2.3.4....1.2.3....0.1.2....1.4.4....1.1.4....2.3.4....2.3.4....2.2.2

..1.3.4.4..0.2.2.4..0.0.1.3..1.3.4.4..0.2.2.4..2.2.4.4..2.2.4.4..0.2.2.4

CROSSREFS

Row 2 is A002620(n+2)

Sequence in context: A145178 A105079 A338162 * A214906 A274228 A321476

Adjacent sequences:  A215179 A215180 A215181 * A215183 A215184 A215185

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Aug 05 2012

STATUS

approved

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Last modified April 10 15:47 EDT 2021. Contains 342845 sequences. (Running on oeis4.)