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A221518 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more, starting with 0. 1
0, 8, 248, 2088, 9940, 33860, 92934, 219352, 463208, 898020, 1626970, 2789864, 4570812, 7206628, 10995950, 16309080, 23598544, 33410372, 46396098, 63325480, 85099940, 112766724, 147533782, 190785368, 244098360, 309259300, 388282154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 7 of A221515.

LINKS

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

FORMULA

Empirical: a(n) = 1*n^6 + 1*n^5 - 29*n^4 + 104*n^3 - 173*n^2 + 136*n - 40 for n>3.

Conjectures from Colin Barker, Aug 06 2018: (Start)

G.f.: 2*x^2*(4 + 96*x + 260*x^2 + 126*x^3 - 136*x^4 + 43*x^5 - 49*x^6 + 19*x^7 - 3*x^8) / (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>10.

(End)

EXAMPLE

Some solutions for n=6:

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

..6....5....3....5....5....4....3....5....6....6....3....6....6....6....3....5

..0....1....0....1....0....6....5....5....2....5....6....1....2....0....0....6

..5....1....2....4....2....6....2....1....4....2....6....0....1....2....5....0

..2....5....4....0....4....0....6....5....2....6....0....6....5....5....1....0

..6....6....5....2....5....0....2....2....4....3....3....5....5....0....6....4

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

CROSSREFS

Cf. A221515.

Sequence in context: A219269 A029751 A035036 * A317519 A300202 A138323

Adjacent sequences:  A221515 A221516 A221517 * A221519 A221520 A221521

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 18 2013

STATUS

approved

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Last modified February 27 17:52 EST 2020. Contains 332307 sequences. (Running on oeis4.)