A246894 Number of length 2+4 0..n arrays with some pair in every consecutive five terms totalling exactly n.

58, 673, 3364, 12481, 33294, 79345, 159688, 303169, 521890, 866881, 1351788, 2057473, 2996854, 4289041, 5943184, 8125825, 10838538, 14305249, 18515380, 23760961, 30013918, 37645873, 46605144, 57355201, 69813874, 84549505

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).

Conjectures from Colin Barker, Nov 07 2018: (Start)

G.f.: x*(58 + 557*x + 1844*x^2 + 4198*x^3 + 3740*x^4 + 2876*x^5 - 268*x^6 - 1486*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).

a(n) = 1 - 72*n + 146*n^2 - 57*n^3 + 31*n^4 + 6*n^5 for n even.

a(n) = -101 + 84*n + 99*n^2 - 61*n^3 + 31*n^4 + 6*n^5 for n odd.

(End)

Example

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

Crossrefs

Row 2 of A246892.

Sequence in context: A249003 A249468 A232378 * A204470 A254954 A172215

Adjacent sequences: A246891 A246892 A246893 * A246895 A246896 A246897

Keyword

nonn

Author

R. H. Hardin, Sep 06 2014

Status

approved