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A241620 Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n. 1
19, 147, 711, 2567, 7586, 19374, 44274, 92697, 180829, 332761, 583089, 980031, 1589108, 2497436, 3818676, 5698689, 8321943, 11918719, 16773163, 23232231, 31715574, 42726410, 56863430, 74833785, 97467201, 125731269, 160747957 (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) = (47/5040)*n^7 + (47/360)*n^6 + (7/9)*n^5 + (23/9)*n^4 + (3599/720)*n^3 + (2093/360)*n^2 + (26/7)*n + 1.

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

G.f.: x*(19 - 5*x + 67*x^2 - 69*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

EXAMPLE

Some solutions for n=5:

..3....3....1....0....2....2....2....3....0....0....0....2....1....5....0....0

..2....2....3....3....2....0....1....2....3....3....5....0....1....0....1....0

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

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

..2....1....0....3....0....1....1....3....1....0....4....0....1....0....1....1

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

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

CROSSREFS

Row 5 of A241619.

Sequence in context: A264679 A200530 A183748 * A069423 A183740 A162872

Adjacent sequences:  A241617 A241618 A241619 * A241621 A241622 A241623

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 26 2014

STATUS

approved

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Last modified February 26 21:50 EST 2020. Contains 332295 sequences. (Running on oeis4.)