OFFSET
2,1
COMMENTS
Number of {0,1} 5 X n matrices (with n at least 2) with one fixed zero entry and no zero rows or columns.
Number of edge covers of a K(5,n) complete bipartite graph (with n at least 2) missing one edge.
LINKS
Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
Index entries for linear recurrences with constant coefficients, signature (57,-1002,6562,-15381,9765).
FORMULA
a(n) = 15*31^(n-1) - 43*15^(n-1) + 46*7^(n-1) - 22*3^(n-1) + 4.
From Stefano Spezia, Jul 04 2020: (Start)
G.f.: 16*x^2*(5 + 140*x + 593*x^2 + 522*x^3)/(1 - 57*x + 1002*x^2 - 6562*x^3 + 15381*x^4 - 9765*x^5).
a(n) = 57*a(n-1) - 1002*a(n-2) + 6562*a(n-3) - 15381*a(n-4) + 9765*a(n-5) for n > 6. (End)
EXAMPLE
For n = 2, a(2) = 80.
MATHEMATICA
Array[15*31^(# - 1) - 43*15^(# - 1) + 46*7^(# - 1) - 22*3^(# - 1) + 4 &, 16, 2] (* Michael De Vlieger, Jun 22 2020 *)
CROSSREFS
Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.
KEYWORD
easy,nonn
AUTHOR
Steven Schlicker, Jun 15 2020
STATUS
approved