A089937 Number of 6 X n matrices with entries {0,1} without adjacent 0's in any row or column. 6th row of A089934.

21, 239, 2999, 36787, 454385, 5598861, 69050253, 851302029, 10496827403, 129422885699, 1595777230271, 19675706193157, 242599324206721, 2991220223776445, 36881397137844409, 454743263319217787, 5606930966068061311, 69132797971282998447

Offset

1,1

Comments

Row/columns 1 through 7 are A000045, A001333, A051736, A051737, A089936, A089937, A089938.

Number of independent vertex sets in the grid graph P_6 X P_n. - Andrew Howroyd, Jun 06 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Formula

G.f.: x*(21 + 71*x - 215*x^2 - 385*x^3 + 668*x^4 + 234*x^5 - 400*x^6 + 9*x^7 + 49*x^8 - 3*x^9 - x^10) / (1 - 8*x - 62*x^2 + 78*x^3 + 375*x^4 - 300*x^5 - 486*x^6 + 385*x^7 + 30*x^8 - 52*x^9 + 2*x^10 + x^11) (conjectured). - Colin Barker, Jun 06 2017

The above conjecture is correct because the order of the recurrence is A089935(6) = 11. - Andrew Howroyd, Dec 24 2019

Crossrefs

Row 6 of A089934.

Cf. A000045, A001333, A051736, A051737, A089935, A089936, A089938.

Sequence in context: A306171 A316426 A317428 * A175843 A198974 A271792

Adjacent sequences: A089934 A089935 A089936 * A089938 A089939 A089940

Keyword

nonn

Author

Marc LeBrun, Nov 15 2003

Extensions

Terms a(17) and beyond from Andrew Howroyd, Jun 06 2017

Status

approved