A086836 On a 3 X 3 board, number of distinct positions of n digits (modulo rotation/reflection).

3, 12, 66, 378, 1890, 7560, 22680, 45360, 45360

Offset

1,1

Comments

Sequence is finite by definition. Last two numbers are naturally 8 times less than 9!, the total number of 3 X 3 squares (not taking into account symmetries).

Links

Table of n, a(n) for n=1..9.

Formula

a(n) = 1/8*([9]_n+4*[3]_n+3*[1]_n) = 3/8*(967680-1145424*n+705596*n^2-256796*n^3+59649*n^4-8936*n^5+834*n^6-44*n^7+n^8)/GAMMA(10-n), where [m]_n=m*(m-1)*...*(m-n+1) is falling factorial. - Vladeta Jovovic, Aug 10 2003

Example

a(1)=3 because there are 3 distinct (corner, side or central ) cells which can be occupied by 1 digit

Crossrefs

Cf. A087074.

Sequence in context: A007017 A183273 A082987 * A074513 A290147 A007871

Adjacent sequences: A086833 A086834 A086835 * A086837 A086838 A086839

Keyword

easy,nonn,fini,full

Author

Zak Seidov, Aug 08 2003

Status

approved