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A249292 Number of length 2+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth 1
26, 168, 660, 2228, 5646, 12600, 25280, 46608, 80334, 131672, 206112, 311352, 455954, 649920, 904884, 1235024, 1654734, 2181960, 2836016, 3638460, 4613010, 5786924, 7188012, 8848968, 10803998, 13090368, 15748356, 18822884, 22359246 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A249290

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4) +a(n-5) -a(n-6) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +a(n-12) -2*a(n-13) +2*a(n-14) +2*a(n-18) -2*a(n-19) +a(n-20) -a(n-21) +a(n-22) -2*a(n-23) +a(n-24) -a(n-26) +a(n-27) -a(n-28) +2*a(n-29) -2*a(n-30) +2*a(n-31) -a(n-32)

Also a polynomial of degree 5 plus a linear quasipolynomial with period 360, the first 12 being:

Empirical for n mod 360 = 0: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n

Empirical for n mod 360 = 1: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (967/60)*n - (113/60)

Empirical for n mod 360 = 2: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n + (8/15)

Empirical for n mod 360 = 3: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (49/20)*n - (3/4)

Empirical for n mod 360 = 4: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n - (26/15)

Empirical for n mod 360 = 5: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (647/60)*n - (125/12)

Empirical for n mod 360 = 6: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n - (114/5)

Empirical for n mod 360 = 7: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (787/60)*n - (653/60)

Empirical for n mod 360 = 8: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n - (20/3)

Empirical for n mod 360 = 9: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (109/20)*n + (117/20)

Empirical for n mod 360 = 10: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n + (20/3)

Empirical for n mod 360 = 11: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (467/60)*n + (707/60)

EXAMPLE

Some solutions for n=10

..4....0....9....7....5....3....9....2....1....3....3....1....1....5....1....4

..7....3....7....5....3....2....5....5....5....2....7....7...10....6....6...10

..4....7....2...10...10....8....6....8....3....1....5...10....1....6....9....3

..3....1....1....8...10....2....5....9....6...10....3....5....9....6...10....6

..7....0....0....2....6....8....9....3....7....9....4....7....7....7....5....0

CROSSREFS

Sequence in context: A200874 A027280 A006354 * A279744 A214353 A283567

Adjacent sequences:  A249289 A249290 A249291 * A249293 A249294 A249295

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 24 2014

STATUS

approved

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Last modified June 25 13:19 EDT 2022. Contains 354851 sequences. (Running on oeis4.)