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 A051737 Number of 4 X n (0,1)-matrices with no consecutive 1's in any row or column. 8
 1, 8, 41, 227, 1234, 6743, 36787, 200798, 1095851, 5980913, 32641916, 178150221, 972290957, 5306478436, 28961194501, 158061670175, 862654025422, 4708111537971, 25695485730239, 140238391149386, 765379824048327, 4177217595760125, 22798023012345528, 124424893212114297 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 N. J. Calkin and H. S. Wilf, The number of independent sets in a grid graph, preprint. N. J. Calkin and H. S. Wilf, The number of independent sets in a grid graph, SIAM J. Discrete Math, 11 (1998) 54-60. Reinhardt Euler, The Fibonacci Number of a Grid Graph and a New Class of Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.6. Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799 (set omega = 1 in Eq. (48)). Index entries for linear recurrences with constant coefficients, signature (4,9,-5,-4,1). FORMULA From Yong Kong (ykong(AT)curagen.com), Dec 24 2000: (Start) a(n) = 4*a(n - 1) + 9*a(n - 2) - 5*a(n - 3) - 4*a(n - 4) + a(n - 5); G.f.: (1 + 4*x - 4*x^3 + x^4)/(1 - 4*x - 9*x^2 + 5*x^3 + 4*x^4 - x^5). (End) a(n) = 2*a(n - 1) + 18*a(n - 2) + 9*a(n - 3) - 23*a(n - 4) - 2*a(n - 5) + 6*a(n - 6) - a(n - 7). MATHEMATICA LinearRecurrence[{4, 9, -5, -4, 1}, {1, 8, 41, 227, 1234}, 24] (* Jean-François Alcover, Nov 05 2017 *) PROG (PARI) Vec((1+4*x-4*x^3+x^4)/(1-4*x-9*x^2+5*x^3+4*x^4-x^5) + O(x^50)) \\ Michel Marcus, Sep 17 2014 CROSSREFS Row 4 of A089934. Cf. A051736. Sequence in context: A037577 A265149 A209822 * A209841 A196927 A188209 Adjacent sequences:  A051734 A051735 A051736 * A051738 A051739 A051740 KEYWORD easy,nonn AUTHOR Stephen G. Penrice (spenrice(AT)ets.org), Dec 06 1999 EXTENSIONS More terms from James A. Sellers, Dec 08 1999 More terms from Michel Marcus, Sep 17 2014 STATUS approved

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Last modified June 16 04:31 EDT 2021. Contains 345055 sequences. (Running on oeis4.)