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Revision History for A215184 (Underlined text is an addition; strikethrough text is a deletion.)

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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.
(history; published version)
#6 by Wesley Ivan Hurt at Mon Apr 26 19:15:28 EDT 2021
STATUS

editing

approved

#5 by Wesley Ivan Hurt at Mon Apr 26 19:15:20 EDT 2021
NAME

Number of 4 X 4 X 4X4X44 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.

COMMENTS

Row 4 of A215182.

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)).

CROSSREFS

Cf. A215182.

STATUS

approved

editing

#4 by R. H. Hardin at Sun Aug 05 06:16:35 EDT 2012
STATUS

editing

approved

#3 by R. H. Hardin at Sun Aug 05 06:16:30 EDT 2012
LINKS

R. H. Hardin, <a href="/A215184/b215184.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Sun Aug 05 06:16:12 EDT 2012
NAME

allocated for R. H. Hardin

Number of 4X4X4 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

DATA

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin Aug 05 2012

STATUS

approved

editing

#1 by R. H. Hardin at Sun Aug 05 06:05:42 EDT 2012
NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved

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