A215184 Number of 4 X 4 X 4 triangular 0..n arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value.

2, 9, 26, 83, 192, 445, 892, 1752, 3136, 5494, 9074, 14716, 22842, 34868, 51570, 75217, 106968, 150289, 207026, 282233, 378516, 503027, 659558, 857984, 1103346, 1408886, 1781610, 2238970, 2789894, 3457002, 4252128, 5204053, 6327530, 7658725, 9216516

Offset

1,1

Comments

Row 4 of A215182.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-2) +3*a(n-3) -2*a(n-4) +2*a(n-6) -6*a(n-7) +9*a(n-8) -12*a(n-9) +10*a(n-10) -7*a(n-11) +3*a(n-12) +6*a(n-13) -12*a(n-14) +19*a(n-15) -21*a(n-16) +20*a(n-17) -14*a(n-18) +3*a(n-19) +3*a(n-20) -14*a(n-21) +20*a(n-22) -21*a(n-23) +19*a(n-24) -12*a(n-25) +6*a(n-26) +3*a(n-27) -7*a(n-28) +10*a(n-29) -12*a(n-30) +9*a(n-31) -6*a(n-32) +2*a(n-33) -2*a(n-35) +3*a(n-36) -2*a(n-37) +2*a(n-38) -a(n-39).

Example

Some solutions for n=4
.....1........2........1........1........2........1........1........1
....1.1......1.3......0.2......1.1......1.3......1.1......0.2......1.1
...1.1.1....1.1.4....0.0.3....0.0.3....0.2.4....1.1.1....0.1.2....0.1.2
..1.1.1.1..0.2.2.4..0.0.1.3..0.0.1.3..0.0.4.4..0.1.1.2..0.0.2.2..0.0.2.2

Crossrefs

Cf. A215182.

Sequence in context: A082289 A014150 A213387 * A136429 A091469 A125670

Adjacent sequences: A215181 A215182 A215183 * A215185 A215186 A215187

Keyword

nonn

Author

R. H. Hardin Aug 05 2012

Status

approved