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A253130 Number of length 2+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero. 1
12, 53, 152, 345, 676, 1197, 1968, 3057, 4540, 6501, 9032, 12233, 16212, 21085, 26976, 34017, 42348, 52117, 63480, 76601, 91652, 108813, 128272, 150225, 174876, 202437, 233128, 267177, 304820, 346301, 391872, 441793, 496332, 555765, 620376, 690457 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (1/3)*n^4 + (8/3)*n^3 + (14/3)*n^2 + (10/3)*n + 1.

Conjectures from Colin Barker, Dec 09 2018: (Start)

G.f.: x*(3 - x)*(4 - x + 2*x^2 - x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

EXAMPLE

Some solutions for n=10:

..7....4....7....9....1....4....7....6....5....4....4....4....6....9....9....1

..2....6...10....0....2....1...10....7....9....6...10....0....6....2....5....6

..0....9....9....1....9....0....9...10....8....8....6....3....7....1....9....3

..4....0....4....3....2....1....5....3....1....6....6....7....2....4....9....2

CROSSREFS

Row 2 of A253129.

Sequence in context: A307916 A280660 A268186 * A213549 A211060 A242514

Adjacent sequences:  A253127 A253128 A253129 * A253131 A253132 A253133

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 27 2014

STATUS

approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)