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

1,1

Comments

Row 5 of A250167

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)

Example

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

Crossrefs

Sequence in context: A191489 A055752 A362234 * A125420 A163690 A268999

Adjacent sequences: A250167 A250168 A250169 * A250171 A250172 A250173

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved