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A241965 Number of length 2+3 0..n arrays with no consecutive four elements summing to more than 2*n. 1
19, 124, 486, 1421, 3437, 7280, 13980, 24897, 41767, 66748, 102466, 152061, 219233, 308288, 424184, 572577, 759867, 993244, 1280734, 1631245, 2054613, 2561648, 3164180, 3875105, 4708431, 5679324, 6804154, 8100541, 9587401, 11284992 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (23/60)*n^5 + (9/4)*n^4 + (21/4)*n^3 + (25/4)*n^2 + (58/15)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(19 + 10*x + 27*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
EXAMPLE
Some solutions for n=4:
..2....1....1....1....1....0....0....3....0....1....4....2....4....2....1....4
..0....2....0....2....1....4....0....3....0....0....3....1....0....0....0....4
..2....1....0....3....0....2....2....0....4....3....0....1....2....1....0....0
..1....0....2....1....2....2....2....1....3....2....0....4....0....4....2....0
..1....1....2....2....4....0....4....3....1....0....0....2....0....2....0....3
CROSSREFS
Row 2 of A241964.
Sequence in context: A070302 A125329 A126487 * A182193 A109669 A164905
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 03 2014
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)