A249985 Number of length 5+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 5*n.

136, 1606, 6856, 22560, 55372, 123154, 237348, 434042, 728724, 1184066, 1817540, 2728080, 3931760, 5574774, 7667096, 10414498, 13814832, 18147086, 23389648, 29909680, 37657444, 47104554, 58163164, 71426938, 86758620, 104892842

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).

Empirical for n mod 2 = 0: a(n) = (1739/240)*n^5 + (3679/96)*n^4 + (859/12)*n^3 + (1121/24)*n^2 - (4/15)*n + 2.

Empirical for n mod 2 = 1: a(n) = (1739/240)*n^5 + (3679/96)*n^4 + (1553/24)*n^3 + (1357/48)*n^2 - (949/240)*n + (45/32).

Empirical g.f.: 2*x*(68 + 667*x + 1618*x^2 + 2559*x^3 + 1402*x^4 + 579*x^5 + 58*x^6 + 4*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4) - Colin Barker, Nov 10 2018.

Example

Some solutions for n=6:
.10....7....1....1....2....8....2....0....0....2....3....3...11....1...11....8
..0...10....6....6....8....0....6....4...12....9....4....0....2....9....1....3
..1...11....7....9....0...11...10....7....6....1...11...12....3....8....5...11
.10....1....0....1....9....7....0...12....6...12....8....4...11....4....0....3
..8....9....9...10....4....1...10....3...10...11....0....2....1...12....7....1
..0....1....1....5....6....2...12...12....2....8...11....7....3....3...11....8

Crossrefs

Row 5 of A249982.

Sequence in context: A023070 A015163 A235190 * A072897 A254703 A333110

Adjacent sequences: A249982 A249983 A249984 * A249986 A249987 A249988

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved