|
| |
|
|
A248538
|
|
Number of length 1+3 0..n arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth.
|
|
1
|
|
|
|
2, 15, 52, 101, 198, 331, 512, 753, 1066, 1439, 1908, 2461, 3110, 3867, 4744, 5729, 6858, 8119, 9524, 11085, 12814, 14699, 16776, 19033, 21482, 24135, 27004, 30077, 33390, 36931, 40712, 44745, 49042, 53591, 58428, 63541, 68942, 74643, 80656, 86969
(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) = 2*a(n-1) - a(n-3) - a(n-4) + 2*a(n-6) - a(n-7).
Empirical for n mod 6 = 0: a(n) = (4/3)*n^3 + n^2 + n + 1.
Empirical for n mod 6 = 1: a(n) = (4/3)*n^3 + n^2 + n - (4/3).
Empirical for n mod 6 = 2: a(n) = (4/3)*n^3 + n^2 + n - (5/3).
Empirical for n mod 6 = 3: a(n) = (4/3)*n^3 + n^2 + n + 4.
Empirical for n mod 6 = 4: a(n) = (4/3)*n^3 + n^2 + n - (13/3).
Empirical for n mod 6 = 5: a(n) = (4/3)*n^3 + n^2 + n + (4/3).
Empirical g.f.: x*(2 + 11*x + 22*x^2 - x^3 + 13*x^4 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)*(1 + x + x^2)). - Colin Barker, Nov 08 2018
|
|
|
EXAMPLE
|
Some solutions for n=6:
..2....0....4....2....0....5....2....3....3....2....5....1....1....5....2....0
..3....2....6....4....3....6....0....5....3....4....2....6....5....1....5....2
..4....4....2....3....4....5....1....1....2....4....0....4....6....0....2....1
..3....2....4....3....5....4....5....3....4....6....1....5....4....2....3....1
|
|
|
CROSSREFS
|
Row 1 of A248537.
Sequence in context: A154565 A066562 A073877 * A248539 A248540 A007972
Adjacent sequences: A248535 A248536 A248537 * A248539 A248540 A248541
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
R. H. Hardin, Oct 08 2014
|
|
|
STATUS
|
approved
|
| |
|
|
