The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A333514 Number of self-avoiding closed paths on an n X 4 grid which pass through four corners ((0,0), (0,3), (n-1,3), (n-1,0)). 2
 1, 3, 11, 49, 229, 1081, 5123, 24323, 115567, 549253, 2610697, 12409597, 58988239, 280398495, 1332867179, 6335755801, 30116890013, 143160058769, 680508623307, 3234784886251, 15376488953815, 73091850448509, 347440733910081, 1651552982759797, 7850625988903223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Also number of self-avoiding closed paths on a 4 X n grid which pass through four corners ((0,0), (0,n-1), (3,n-1), (3,0)). LINKS Index entries for linear recurrences with constant coefficients, signature (7,-12,7,-3,-2). FORMULA G.f.: x^2*(1-4*x+2*x^2+x^3)/(1-7*x+12*x^2-7*x^3+3*x^4+2*x^5). a(n) = 7*a(n-1) - 12*a(n-2) + 7*a(n-3) - 3*a(n-4) - 2*a(n-5) for n > 6. EXAMPLE a(2) = 1; +--*--*--+ | | +--*--*--+ a(3) = 3; +--*--*--+ +--*--*--+ +--* *--+ | | | | | | | | * *--* * * * * *--* * | | | | | | | | +--* *--+ +--*--*--+ +--*--*--+ a(4) = 11; +--*--*--+ +--*--*--+ +--*--*--+ | | | | | | *--*--* * *--* *--* *--* * | | | | | | *--*--* * *--* *--* *--* * | | | | | | +--*--*--+ +--*--*--+ +--*--*--+ +--*--*--+ +--*--*--+ +--*--*--+ | | | | | | * *--*--* * *--* * * *--* | | | | | | | | * *--*--* * * * * * *--* | | | | | | | | +--*--*--+ +--* *--+ +--*--*--+ +--*--*--+ +--*--*--+ +--* *--+ | | | | | | | | * * * * * *--* * | | | | | | * *--* * * * * *--* * | | | | | | | | | | +--* *--+ +--*--*--+ +--* *--+ +--* *--+ +--* *--+ | | | | | | | | * *--* * * * * * | | | | | | * * * *--* * | | | | +--*--*--+ +--*--*--+ PROG (PARI) N=40; x='x+O('x^N); Vec(x^2*(1-4*x+2*x^2+x^3)/(1-7*x+12*x^2-7*x^3+3*x^4+2*x^5)) (Python) # Using graphillion from graphillion import GraphSet import graphillion.tutorial as tl def A333513(n, k): universe = tl.grid(n - 1, k - 1) GraphSet.set_universe(universe) cycles = GraphSet.cycles() for i in [1, k, k * (n - 1) + 1, k * n]: cycles = cycles.including(i) return cycles.len() def A333514(n): return A333513(4, n) print([A333514(n) for n in range(2, 15)]) CROSSREFS Column k=4 of A333513. Sequence in context: A025539 A172440 A254536 * A268414 A074528 A246985 Adjacent sequences: A333511 A333512 A333513 * A333515 A333516 A333517 KEYWORD nonn AUTHOR Seiichi Manyama, Mar 25 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 26 23:26 EDT 2023. Contains 361553 sequences. (Running on oeis4.)