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A163030
Number of n X 4 binary arrays with all 1s connected and a path of 1s from top row to bottom row.
3
10, 88, 920, 9362, 94280, 947760, 9528128, 95797726, 963186740, 9684246062, 97369020768, 978984263266, 9843070964036, 98965887676178, 995039757124590, 10004498940354450, 100588944638377056, 1011358574138112578, 10168574381191282946, 102238620000802749640, 1027945022362688224996
OFFSET
1,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..800 (terms 1..44 from R. H. Hardin)
Index entries for linear recurrences with constant coefficients, signature (15,-59,97,-19,-210,222,22,-113,7,-71,13,1).
FORMULA
Empirical: a(n)= 15*a(n-1) -59*a(n-2) +97*a(n-3) -19*a(n-4) -210*a(n-5) +222*a(n-6) +22*a(n-7) -113*a(n-8) +7*a(n-9) -71*a(n-10) +13*a(n-11) +a(n-12). - R. J. Mathar, Aug 11 2009
For a proof see the Goodman-Strauss links. - N. J. A. Sloane, May 22 2020
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 - 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, Dec 24 2025
CROSSREFS
Column 4 of A359574.
Sequence in context: A287828 A264320 A298134 * A302149 A269008 A000826
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jul 20 2009
STATUS
approved