OFFSET
0,2
COMMENTS
Number of 4 X n binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..10000
R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
Vladeta Jovovic, Binary matrices up to row and column permutations
Index entries for linear recurrences with constant coefficients, signature (5, -7, -1, 5, -1, 21, -33, 0, -4, 8, 68, -57, -3, -57, 13, 100, -32, 32, -100, -13, 57, 3, 57, -68, -8, 4, 0, 33, -21, 1, -5, 1, 7, -5, 1).
FORMULA
G.f.: (x^20 - x^19 + 4*x^18 + 9*x^17 + 23*x^16 + 39*x^15 + 90*x^14 + 131*x^13 + 204*x^12 + 238*x^11 + 252*x^10 + 238*x^9 + 204*x^8 + 131*x^7 + 90*x^6 + 39*x^5 + 23*x^4 + 9*x^3 + 4*x^2 - x + 1)/((1 - x^4)^3*(1 - x^3)^4*(1 - x^2)^3*(1 - x)^5).
a(n) ~ n^14/2092278988800. - Stefano Spezia, Aug 08 2022
a(n) = n^14/2092278988800 + n^13/19926466560 + n^12/418037760 + n^11/14598144 + 689*n^10/522547200 + 253*n^9/13934592 + 2184839*n^8/11705057280 + 10313*n^7/6967296 + 2319707*n^6/250822656 + 1817221*n^5/39813120 + 2405336243*n^4/13795246080 + 151784975*n^3/306561024 + 93746545019*n^2/95103590400 + 924100468541*n/717352796160 + 1 + (n^2/486 + 5*n/162 + 233/2187)*floor(n/3) + (n^2/256 + 15*n/256 + 101/512)*floor(n/4) - (n^3/1458 + 7*n^2/486 + 22*n/243 + 356/2187)*floor((n+1)/3) + (n^5/122880 + 5*n^4/16384 + 125*n^3/24576 + 359*n^2/8192 + 10967*n/61440 + 8461/32768)*floor(n/2) + (n/256 + 15/512)*floor((n+1)/4). - Vaclav Kotesovec, Aug 09 2022
PROG
(PARI) Vec(G(4, x)*(1 - x) + O(x^40)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Jun 03 2000
a(0)=1 prepended by Alois P. Heinz, Aug 08 2022
STATUS
approved