A250562 Number of length 3+2 0..n arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero

14, 83, 302, 761, 1648, 3125, 5446, 8843, 13662, 20173, 28836, 39973, 54102, 71647, 93210, 119221, 150416, 187305, 230650, 281051, 339378, 406245, 482652, 569257, 667098, 776983, 900018, 1036969, 1189124, 1357341, 1542894, 1746747, 1970290

Offset

1,1

Comments

Row 3 of A250561

Links

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

Formula

Empirical: a(n) = a(n-1) -a(n-2) +2*a(n-3) +a(n-5) -2*a(n-7) -3*a(n-9) +a(n-10) -a(n-11) +3*a(n-12) +2*a(n-14) -a(n-16) -2*a(n-18) +a(n-19) -a(n-20) +a(n-21)

also a quadratic polynomial plus a linear quasipolynomial with period 60, the first 12 being:

Empirical for n mod 60 = 0: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (23/30)*n + 1

Empirical for n mod 60 = 1: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (1853/1080)*n + (251/270)

Empirical for n mod 60 = 2: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (127/270)*n + (211/270)

Empirical for n mod 60 = 3: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (337/120)*n + (13/5)

Empirical for n mod 60 = 4: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (47/270)*n + (283/135)

Empirical for n mod 60 = 5: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (2173/1080)*n + (35/54)

Empirical for n mod 60 = 6: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (23/30)*n + (13/10)

Empirical for n mod 60 = 7: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (2393/1080)*n - (77/135)

Empirical for n mod 60 = 8: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (127/270)*n + (281/135)

Empirical for n mod 60 = 9: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (277/120)*n + (33/10)

Empirical for n mod 60 = 10: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (47/270)*n + (43/54)

Empirical for n mod 60 = 11: a(n) = (329/216)*n^4 + (4747/1080)*n^3 + (1957/360)*n^2 + (2713/1080)*n - (7/135)

Example

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

Crossrefs

Sequence in context: A199912 A082971 A176010 * A166819 A108683 A323415

Adjacent sequences: A250559 A250560 A250561 * A250563 A250564 A250565

Keyword

nonn

Author

R. H. Hardin, Nov 25 2014

Status

approved