A212783 Half the number of 0..n arrays of length 4 with second differences nonzero.

5, 27, 99, 252, 546, 1034, 1803, 2925, 4517, 6670, 9528, 13204, 17869, 23655, 30763, 39344, 49626, 61782, 76067, 92673, 111885, 133914, 159072, 187592, 219813, 255987, 296483, 341572, 391650, 447010, 508075, 575157, 648709, 729062, 816696, 911964

Offset

1,1

Comments

Row 2 of A212782.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) - a(n-4) + a(n-5) + 3*a(n-6) - a(n-7) - 2*a(n-8) + a(n-9).

Empirical g.f.: x*(5 + 17*x + 40*x^2 + 42*x^3 + 29*x^4 + 9*x^5 + 2*x^6) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jul 21 2018

Example

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

Crossrefs

Cf. A212782.

Sequence in context: A085740 A338996 A349919 * A226315 A201436 A202508

Adjacent sequences: A212780 A212781 A212782 * A212784 A212785 A212786

Keyword

nonn

Author

R. H. Hardin, May 27 2012

Status

approved