A248463 Number of length 2+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

10, 36, 148, 380, 862, 1652, 2956, 4860, 7642, 11400, 16488, 23044, 31482, 41952, 54956, 70672, 89662, 112128, 138708, 169632, 205610, 246884, 294240, 347960, 408890, 477324, 554196, 639828, 735214, 840700, 957356, 1085556, 1226442

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).

Empirical for n mod 12 = 0: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 1: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (5/2).

Empirical for n mod 12 = 2: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n - (4/3).

Empirical for n mod 12 = 3: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (3/2).

Empirical for n mod 12 = 4: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 5: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (7/6).

Empirical for n mod 12 = 6: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 7: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (3/2).

Empirical for n mod 12 = 8: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n - (4/3).

Empirical for n mod 12 = 9: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (5/2).

Empirical for n mod 12 = 10: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.

Empirical for n mod 12 = 11: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (17/6).

Empirical g.f.: 2*x*(5 + 8*x + 38*x^2 + 47*x^3 + 69*x^4 + 48*x^5 + 42*x^6 + 17*x^7 + 14*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 08 2018

Example

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

Crossrefs

Row 2 of A248461.

Sequence in context: A051959 A117327 A153371 * A169880 A282554 A240151

Adjacent sequences: A248460 A248461 A248462 * A248464 A248465 A248466

Keyword

nonn

Author

R. H. Hardin, Oct 06 2014

Status

approved