A250170 Number of length 5+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

32, 373, 1880, 7109, 19896, 49037, 103556, 203615, 364900, 624811, 1006084, 1570791, 2347840, 3431579, 4856212, 6757417, 9171308, 12285541, 16134624, 20968689, 26816804, 34003157, 42544984, 52855367, 64932468, 79290519, 95903144

Offset: 1

Author

R. H. Hardin, Nov 13 2014

Keywords

• nonn

Comments

Row 5 of A250167

Examples

			Some solutions for n=6
..6....3....3....3....4....6....4....3....5....1....6....4....1....0....6....3
..3....1....0....1....6....4....3....3....1....5....6....3....4....0....4....5
..1....6....2....2....5....6....0....2....2....5....4....3....5....3....1....1
..0....2....4....4....0....0....3....4....3....4....0....2....3....1....2....1
..5....1....1....6....2....0....5....2....1....3....4....1....4....2....6....1
..6....1....5....3....2....6....6....3....1....5....6....2....3....0....6....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..66

Formula

Empirical: a(n) = a(n-2) +a(n-3) +2*a(n-4) -a(n-6) -3*a(n-7) -3*a(n-8) -a(n-9) +3*a(n-11) +4*a(n-12) +3*a(n-13) -a(n-15) -3*a(n-16) -3*a(n-17) -a(n-18) +2*a(n-20) +a(n-21) +a(n-22) -a(n-24)

Empirical: also a polynomial of degree 5 plus a cubic quasipolynomial with period 60, the first 12 being:

Empirical for n mod 60 = 0: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n + 1

Empirical for n mod 60 = 1: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (223/64)*n + (457247/8640)

Empirical for n mod 60 = 2: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (2339/36)*n + (7721/270)

Empirical for n mod 60 = 3: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (703/64)*n + (7753/64)

Empirical for n mod 60 = 4: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (1141/135)

Empirical for n mod 60 = 5: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (7639/576)*n + (217043/1728)

Empirical for n mod 60 = 6: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (157/10)

Empirical for n mod 60 = 7: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (703/64)*n + (893567/8640)

Empirical for n mod 60 = 8: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (2339/36)*n + (1223/27)

Empirical for n mod 60 = 9: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (223/64)*n + (24653/320)

Empirical for n mod 60 = 10: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (1531/54)

Empirical for n mod 60 = 11: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (11959/576)*n + (1493887/8640)