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A241967 Number of length 4+3 0..n arrays with no consecutive four elements summing to more than 2*n. 1
57, 775, 5211, 23320, 80132, 228826, 569874, 1277427, 2634115, 5075433, 9244885, 16061058, 26797798, 43178660, 67486804, 102691509, 152592477, 221983099, 316833855, 444497020, 613933848, 835965406, 1123548230, 1492075975 (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) = (293/1260)*n^7 + (691/360)*n^6 + (2443/360)*n^5 + (121/9)*n^4 + (5857/360)*n^3 + (4369/360)*n^2 + (2189/420)*n + 1.

Conjectures from Colin Barker, Oct 31 2018: (Start)

G.f.: x*(57 + 319*x + 607*x^2 + 140*x^3 + 70*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=4:

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

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

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

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

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

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

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

CROSSREFS

Row 4 of A241964.

Sequence in context: A232875 A084220 A060891 * A098995 A210156 A210149

Adjacent sequences:  A241964 A241965 A241966 * A241968 A241969 A241970

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 03 2014

STATUS

approved

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Last modified September 25 06:19 EDT 2022. Contains 356959 sequences. (Running on oeis4.)