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

Author

Marc LeBrun, Nov 15 2003

Keywords

• nonn

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

Crossrefs

Row 6 of A089934.

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

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

Extensions

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