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A224392 Number of 3 X n 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing. 1
64, 1000, 6094, 27790, 102232, 319769, 881519, 2196522, 5038720, 10788462, 21789398, 41858498, 76994510, 136338455, 233448747, 387963222, 627730762, 991506308, 1532314870, 2321602662, 3454306716, 5054988261, 7285189791 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A224391.

LINKS

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

FORMULA

Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9731/30240)*n^7 + (1283/720)*n^6 + (52457/8640)*n^5 + (776/45)*n^4 + (294499/11340)*n^3 + (28837/2520)*n^2 + (8207/126)*n - 18 for n>1.

Conjectures from Colin Barker, Aug 30 2018: (Start)

G.f.: x*(64 + 360*x - 1026*x^2 + 4170*x^3 - 7998*x^4 + 10591*x^5 - 9351*x^6 + 5629*x^7 - 2165*x^8 + 478*x^9 - 46*x^10) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.

(End)

EXAMPLE

Some solutions for n=3:

..0..1..1....0..1..1....1..1..2....0..0..1....0..1..1....1..1..3....0..2..2

..2..2..2....0..0..1....2..3..3....2..2..2....2..2..2....1..2..3....1..2..3

..0..2..2....0..0..0....1..1..2....1..3..3....0..0..1....1..3..3....0..3..3

CROSSREFS

Cf. A224391.

Sequence in context: A224162 A224413 A016959 * A224025 A270272 A297612

Adjacent sequences:  A224389 A224390 A224391 * A224393 A224394 A224395

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 05 2013

STATUS

approved

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Last modified November 15 08:37 EST 2019. Contains 329144 sequences. (Running on oeis4.)