A059524 Number of nonzero 4 X n binary arrays with all 1's connected.

0, 10, 108, 1126, 11506, 116166, 1168586, 11749134, 118127408, 1187692422, 11941503498, 120064335342, 1207171430452, 12137349489598, 122033415224922, 1226969238084836, 12336404001299200, 124034783402890620, 1247091736942594618, 12538723071673581562

Offset

0,2

Comments

Old name was "Number of 4 X n checkerboards in which the set of red squares is edge connected".

The number of connected (non-null) induced subgraphs in the grid graph P_4 X P_n. - Andrew Howroyd, May 20 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (17,-90,230,-272,-75,623,-632,65,255,-198,162,-96,11,1).

Formula

Empirical g.f.: 2*x*(1 + x)*(5 - 36*x + 131*x^2 - 239*x^3 + 131*x^4 + 94*x^5 - 157*x^6 + 61*x^7 - 73*x^8 + 18*x^9 + x^10) / ((1 - x)^2*(1 - 15*x + 59*x^2 - 97*x^3 + 19*x^4 + 210*x^5 - 222*x^6 - 22*x^7 + 113*x^8 - 7*x^9 + 71*x^10 - 13*x^11 - x^12)). - Colin Barker, Oct 11 2017

The recurrence is correct. See A287151. - Andrew Howroyd, Dec 18 2024

Example

a(1) = 10 because there are 4 positions to place a single 1, 3 ways to place a pair of adjacent 1's, 2 ways to place a triple of connected 1's, and 1 way for the all-1's array: 4+3+2+1=10. - R. J. Mathar, Mar 13 2023

Crossrefs

Row 4 of A287151.

Cf. A059020, A059021.

Sequence in context: A218061 A339117 A157084 * A190957 A163206 A246073

Adjacent sequences: A059521 A059522 A059523 * A059525 A059526 A059527

Keyword

nonn

Author

David Radcliffe, Jan 21 2001

Extensions

Clearer name from R. H. Hardin, Jul 06 2009

a(16) corrected by Andrew Howroyd, May 20 2017

Status

approved