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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

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Last modified January 31 17:34 EST 2023. Contains 359979 sequences. (Running on oeis4.)