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A195523 Number of lower triangles of a 5 X 5 -n..n array with all row and column sums zero. 1
199, 3753, 27267, 121367, 401565, 1089411, 2563933, 5423365, 10557163, 19228309, 33165903, 54668043, 86714993, 133092639, 198526233, 288824425, 411033583, 573602401, 786556795, 1061685087, 1412733477, 1855611803, 2408609589 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 5 of A195522.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..175

FORMULA

Empirical: a(n) = (643/45)*n^6 + (643/15)*n^5 + (2165/36)*n^4 + (293/6)*n^3 + (4423/180)*n^2 + (73/10)*n + 1.

Conjectures from Colin Barker, May 08 2018: (Start)

G.f.: x*(199 + 2360*x + 5175*x^2 + 2346*x^3 + 213*x^4 - 6*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

EXAMPLE

Some solutions for n=4:

..0..........0..........0..........0..........0..........0..........0

..0.0.......-2.2.......-3.3........0.0.......-3.3........3-3........3-3

..0-3.3.....-2.4-2.....-2-1.3......2-2.0......0-1.1.....-3.0.3......2.0-2

..0.3.0-3....2-2.4-4....4-1-4.1....0-1.2-1....1.0-1.0....4-1.1-4...-4-1.4.1

..0.0-3.3.0..2-4-2.4.0..1-1.1-1.0.-2.3-2.1.0..2-2.0.0.0.-4.4-4.4.0.-1.4-2-1.0

CROSSREFS

Cf. A195522.

Sequence in context: A324628 A216346 A289819 * A163712 A069244 A052355

Adjacent sequences:  A195520 A195521 A195522 * A195524 A195525 A195526

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 20 2011

STATUS

approved

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Last modified January 20 23:24 EST 2020. Contains 331104 sequences. (Running on oeis4.)