A265992 Number of 2 X n integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

1, 1, 2, 2, 4, 6, 7, 11, 15, 26, 48, 82, 135, 227, 375, 634, 1088, 1850, 3135, 5315, 8983, 15218, 25832, 43818, 74319, 126027, 213615, 362162, 614120, 1041346, 1765847, 2994267, 5076959, 8608474, 14596640, 24750370, 41967671, 71161491, 120662599

Offset

1,3

Links

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

Formula

Empirical: a(n) = 3*a(n-3) + a(n-4) + 2*a(n-5) + 2*a(n-6) + 3*a(n-7) + 2*a(n-8) - 4*a(n-9) - 4*a(n-10) - 4*a(n-11) for n>14.

Empirical g.f.: x*(1 + x + 2*x^2 - x^3 - 3*x^5 - 5*x^6 - 12*x^7 - 20*x^8 - 17*x^9 - 14*x^10 + 4*x^13) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - x - 2*x^3)*(1 + x^2 + 2*x^4)). - Colin Barker, Jan 09 2019

Example

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

Crossrefs

Row 2 of A265991.

Sequence in context: A227560 A046639 A178702 * A089284 A297106 A357877

Adjacent sequences: A265989 A265990 A265991 * A265993 A265994 A265995

Keyword

nonn

Author

R. H. Hardin, Dec 19 2015

Status

approved