A251429 Number of length 2+2 0..n arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

12, 41, 116, 237, 432, 725, 1128, 1641, 2316, 3145, 4148, 5357, 6776, 8413, 10328, 12489, 14924, 17689, 20764, 24149, 27928, 32061, 36568, 41513, 46868, 52641, 58924, 65653, 72856, 80621, 88896, 97681, 107092, 117057, 127596, 138805, 150624, 163061

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) + a(n-10) - a(n-11).

Empirical for n mod 12 = 0: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1

Empirical for n mod 12 = 1: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (97/54)

Empirical for n mod 12 = 2: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)

Empirical for n mod 12 = 3: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (11/2)

Empirical for n mod 12 = 4: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)

Empirical for n mod 12 = 5: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (113/54)

Empirical for n mod 12 = 6: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + 1

Empirical for n mod 12 = 7: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (313/54)

Empirical for n mod 12 = 8: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (43/27)

Empirical for n mod 12 = 9: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (3/2)

Empirical for n mod 12 = 10: a(n) = (79/27)*n^3 + (29/18)*n^2 + (17/3)*n + (35/27)

Empirical for n mod 12 = 11: a(n) = (79/27)*n^3 + (29/18)*n^2 + (43/9)*n + (329/54)

Empirical g.f.: x*(12 + 29*x + 75*x^2 + 97*x^3 + 125*x^4 + 114*x^5 + 98*x^6 + 55*x^7 + 27*x^8 + x^9 - x^10) / ((1 - x)^4*(1 + x)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 29 2018

Example

Some solutions for n=10:
..1....1....5....1....6....1....1....0....5....4....8....2....7....8....0....6
..7....8...10....7....4....6....3....3....6....6....3....6....2....6....6....7
.10....3....7....3....3...10....5....1....3....7....9....5...10....6....2....1
..7....7....8....9....6....1....1....4....5....4....1....9....7....8....5....9

Crossrefs

Row 2 of A251428.

Sequence in context: A330826 A222806 A375804 * A114072 A244793 A218712

Adjacent sequences: A251426 A251427 A251428 * A251430 A251431 A251432

Keyword

nonn

Author

R. H. Hardin, Dec 02 2014

Status

approved