A089938 Number of 7 X n matrices with entries {0,1} without adjacent 0's in any row or column. 7th row of A089934.

34, 577, 10897, 200798, 3729091, 69050253, 1280128950, 23720149995, 439621976195, 8147000813446, 150985649174085, 2798109826697003, 51855860689753372, 961012671564107667, 17809889025037476097, 330060028036299469334, 6116807668464485142495

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_7 X P_n. - Andrew Howroyd, Jun 06 2017

Links

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

Crossrefs

Cf. A000045, A001333, A051736, A051737, A089936, A089937, A089934.

Formula

O.g.f.: - (X - 1)*(X^19 + 10*X^18 - 58*X^17 - 576*X^16 + 651*X^15 + 8054*X^14 - 5381*X^13 - 42910*X^12 + 32530*X^11 + 90357*X^10 - 90813*X^9 - 52366*X^8 + 79558*X^7 - 8263*X^6 - 13918*X^5 + 2501*X^4 + 894*X^3 - 94*X^2 - 26*X - 1)/(X^21 + 9*X^20 - 87*X^19 - 546*X^18 + 2227*X^17 + 9369*X^16 - 25564*X^15 - 54187*X^14 + 139011*X^13 + 100779*X^12 - 340142*X^11 + 21372*X^10 + 308107*X^9 - 127405*X^8 - 82823*X^7 + 48558*X^6 + 6975*X^5 - 5659*X^4 - 210*X^3 + 203*X^2 + 9*X - 1)

Extensions

Terms a(16) and beyond from Andrew Howroyd, Jun 06 2017