A201089 Number of -n..n arrays of 4 elements with first and second differences also in -n..n.

25, 175, 651, 1759, 3899, 7581, 13405, 22085, 34421, 51331, 73815, 102995, 140071, 186369, 243289, 312361, 395185, 493495, 609091, 743911, 899955, 1079365, 1284341, 1517229, 1780429, 2076491, 2408015, 2777755, 3188511, 3643241, 4144945, 4696785

Offset

1,1

Comments

Row 4 of A201088.

Links

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

Formula

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

Empirical: -x*(25+100*x+151*x^2+106*x^3+23*x^4-2*x^5+x^6) / ( (1+x)^2*(x-1)^5 ). - R. J. Mathar, Nov 27 2011

Conjectures from Colin Barker, Feb 14 2018: (Start)

a(n) = (101*n^4 + 202*n^3 + 190*n^2 + 92*n + 24) / 24 for n even.

a(n) = (101*n^4 + 202*n^3 + 190*n^2 + 86*n + 21) / 24 for n odd.

(End)

Example

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

Crossrefs

Sequence in context: A213546 A145964 A020250 * A020277 A200671 A042212

Adjacent sequences: A201086 A201087 A201088 * A201090 A201091 A201092

Keyword

nonn

Author

R. H. Hardin, Nov 26 2011

Status

approved