A249657 Number of length 1+4 0..n arrays with every five consecutive terms having four times some element equal to the sum of the remaining four.

2, 53, 164, 485, 1046, 2077, 3708, 6149, 9610, 14441, 20832, 29173, 39794, 53105, 69476, 89417, 113318, 141769, 175260, 214361, 259642, 311813, 371424, 439225, 515906, 602237, 698948, 806909, 926870, 1059781, 1206492, 1367933, 1545034

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-6) - 2*a(n-7) + 3*a(n-8) - 3*a(n-9) + a(n-10).

Empirical for n mod 12 = 0: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n + 1

Empirical for n mod 12 = 1: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n - (53/12)

Empirical for n mod 12 = 2: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n + (23/3)

Empirical for n mod 12 = 3: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n - (31/4)

Empirical for n mod 12 = 4: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n + (43/3)

Empirical for n mod 12 = 5: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n - (133/12)

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

Empirical for n mod 12 = 7: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n + (67/12)

Empirical for n mod 12 = 8: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n + (23/3)

Empirical for n mod 12 = 9: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n - (71/4)

Empirical for n mod 12 = 10: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n + (43/3)

Empirical for n mod 12 = 11: a(n) = (5/4)*n^4 + (5/3)*n^3 + (5/2)*n^2 + n - (13/12)

Empirical g.f.: x*(2 + 47*x + 11*x^2 + 148*x^3 - 19*x^4 + 172*x^5 - 31*x^6 + 32*x^7 - 3*x^8 + x^9) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 09 2018

Example

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

Crossrefs

Row 1 of A249656.

Sequence in context: A212889 A041337 A139844 * A249658 A249659 A249660

Adjacent sequences: A249654 A249655 A249656 * A249658 A249659 A249660

Keyword

nonn

Author

R. H. Hardin, Nov 03 2014

Status

approved