A214595 T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row having the same average value

2, 3, 2, 4, 5, 2, 5, 8, 23, 2, 6, 13, 62, 401, 2, 7, 18, 157, 1862, 20351, 2, 8, 25, 312, 10177, 187862, 2869211, 2, 9, 32, 601, 33352, 3330677, 63120962, 1127599139, 2, 10, 41, 986, 103651, 20608352, 5495329427, 71200442882, 1248252244661, 2, 11, 50, 1619

Offset

1,1

Comments

Table starts

.2.....3......4.......5........6.........7.........8..........9.........10

.2.....5......8......13.......18........25........32.........41.........50

.2....23.....62.....157......312.......601.......986.......1619.......2426

.2...401...1862...10177....33352....103651....250042.....589763....1199614

.2.20351.187862.3330677.20608352.121537201.493575042.1877543213.5767190924

Links

R. H. Hardin, Table of n, a(n) for n = 1..1475

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: (order 12 antisymmetric)

n=4: (order 32 symmetric)

n=5: (order 84 symmetric)

Example

Some solutions for n=4 k=4
.....2........1........2........2........2........2........2........2
....3.1......0.2......2.2......3.1......2.2......1.3......4.0......4.0
...3.2.1....0.3.0....3.2.1....2.4.0....0.2.4....3.0.3....1.2.3....4.0.2
..2.2.3.1..2.1.0.1..1.2.4.1..4.2.2.0..1.4.3.0..4.0.2.2..3.2.3.0..4.0.4.0

Crossrefs

Row 2 is A000982(n+1)

Sequence in context: A226208 A304743 A214540 * A357255 A136181 A265110

Adjacent sequences: A214592 A214593 A214594 * A214596 A214597 A214598

Keyword

nonn,tabl

Author

R. H. Hardin Jul 22 2012

Status

approved