A163004 Number of n X 4 binary arrays with all 1s connected and a path of 1s from upper left corner to lower right corner.

1, 20, 234, 2423, 24455, 245972, 2473317, 24868730, 250043151, 2514035445, 25277060955, 254144975454, 2555267942068, 25691612225457, 258313003017344, 2597174783771339, 26112958991681036, 262549379235881855, 2639768880965112397, 26541215847370455067, 266855232568194615445

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..800 (first 44 terms from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (20,-141,496,-888, 284,2212,-4360,1585, 5060,-6422,-828,4409, -564,-804,-992,-816, 128,99,-12,-1).

Formula

G.f.: x*(1 - 25*x^2 + 67*x^3 - 43*x^4 - 73*x^5 + 124*x^6 + 50*x^7 + 51*x^8 - 157*x^9 - 134*x^10 - 76*x^11 - 249*x^12 - 211*x^13 - 77*x^14 + 15*x^15 + x^17)/((1 + x)*(1 - 2*x - x^2)*(1 - 4*x + 6*x^2 - 4*x^3 - 4*x^4 + x^5)*(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)). - Andrew Howroyd, Oct 27 2025

Crossrefs

Row 4 of A359573.

Sequence in context: A004315 A253010 A074334 * A278320 A061139 A061121

Adjacent sequences: A163001 A163002 A163003 * A163005 A163006 A163007

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jul 20 2009

Status

approved