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A241622 Number of length 7+2 0..n arrays with no consecutive three elements summing to more than n. 1
41, 556, 4175, 21631, 86828, 289248, 835812, 2159025, 5093737, 11151140, 22925695, 44678543, 83149600, 148659968, 256576512, 429221457, 698321649, 1108104700, 1719162599, 2613217519, 3898939484, 5718981280, 8258412500, 11754751905 (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) = (131/60480)*n^9 + (131/3360)*n^8 + (3137/10080)*n^7 + (347/240)*n^6 + (12407/2880)*n^5 + (4097/480)*n^4 + (169957/15120)*n^3 + (7963/840)*n^2 + (487/105)*n + 1.

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

G.f.: x*(41 + 146*x + 460*x^2 - 19*x^3 + 283*x^4 - 209*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

EXAMPLE

Some solutions for n=5:

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

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

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

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

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

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

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

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

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

CROSSREFS

Row 7 of A241619.

Sequence in context: A208048 A298839 A301399 * A276251 A298627 A078947

Adjacent sequences:  A241619 A241620 A241621 * A241623 A241624 A241625

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 26 2014

STATUS

approved

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)