|
|
A249985
|
|
Number of length 5+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 5*n.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|