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 A138979 Number of 4 X n matrices containing a 1 in the top left entry, all entries are integer values and adjacent entries differ by at most 1. 5
 27, 771, 22979, 690437, 20780181, 625649047, 18838482047, 567241901289, 17080173559277, 514300085627023, 15486061794514775, 466299978310573033, 14040733816061115637, 422779788989982722559, 12730299739840800975879, 383321378409770250813777 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Horizontally or vertically adjacent entries can differ by at most 1. Diagonally adjacent entries thus differ by at most 2. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..600 FORMULA a(n)=b(n)+c(n)+d(n)+e(n)+f(n)+g(n)+h(n)+j(n)+k(n)+l(n), where b(1)=2,c(1)=4,d(1)=4,e(1)=2,f(1)=4,g(1)=2,h(1)=2,j(1)=4,k(1)=2,l(1)=1 b(n+1)=3*b(n)+2*c(n)+1*d(n)+2*e(n)+1*f(n)+0*g(n)+1*h(n)+0*j(n)+1*k(n)+0*l(n) c(n+1)=4*b(n)+5*c(n)+3*d(n)+4*e(n)+3*f(n)+2*g(n)+2*h(n)+3*j(n)+4*k(n)+4*l(n) d(n+1)=2*b(n)+3*c(n)+5*d(n)+2*e(n)+4*f(n)+4*g(n)+4*h(n)+4*j(n)+4*k(n)+4*l(n) e(n+1)=2*b(n)+2*c(n)+1*d(n)+3*e(n)+2*f(n)+2*g(n)+2*h(n)+2*j(n)+2*k(n)+2*l(n) f(n+1)=2*b(n)+3*c(n)+4*d(n)+4*e(n)+7*f(n)+6*g(n)+6*h(n)+6*j(n)+6*k(n)+8*l(n) g(n+1)=0*b(n)+1*c(n)+2*d(n)+2*e(n)+3*f(n)+4*g(n)+2*h(n)+3*j(n)+2*k(n)+4*l(n) h(n+1)=1*b(n)+1*c(n)+2*d(n)+2*e(n)+3*f(n)+2*g(n)+4*h(n)+3*j(n)+2*k(n)+4*l(n) j(n+1)=0*b(n)+3*c(n)+4*d(n)+4*e(n)+6*f(n)+6*g(n)+6*h(n)+7*j(n)+6*k(n)+8*l(n) k(n+1)=1*b(n)+2*c(n)+2*d(n)+2*e(n)+3*f(n)+2*g(n)+2*h(n)+3*j(n)+4*k(n)+4*l(n) l(n+1)=0*b(n)+1*c(n)+1*d(n)+1*e(n)+2*f(n)+2*g(n)+2*h(n)+2*j(n)+2*k(n)+3*l(n). G.f.: -x*(-27 +116*x^9 -206*x^8 +5284*x^6 -2464*x^7 -154*x^5 +6514*x^3 -6915*x^4 -2540*x^2 +444*x) / (1 -45*x -1942*x^8 +528*x^2 -278*x^9 -2592*x^3 +112*x^10 +5997*x^4 -5689*x^5 -812*x^6 +4760*x^7). - Alois P. Heinz, Sep 02 2014 MAPLE a:= n-> (Matrix([2, 4, 4, 2, 4, 2, 2, 4, 2, 1]). Matrix([[3, 4, 2, 2, 2, 0, 1, 0, 1, 0], [2, 5, 3, 2, 3, 1, 1, 3, 2, 1], [1, 3, 5, 1, 4, 2, 2, 4, 2, 1], [2, 4, 2, 3, 4, 2, 2, 4, 2, 1], [1, 3, 4, 2, 7, 3, 3, 6, 3, 2], [0, 2, 4, 2, 6, 4, 2, 6, 2, 2], [1, 2, 4, 2, 6, 2, 4, 6, 2, 2], [0, 3, 4, 2, 6, 3, 3, 7, 3, 2], [1, 4, 4, 2, 6, 2, 2, 6, 4, 2], [0, 4, 4, 2, 8, 4, 4, 8, 4, 3]])^(n-1) .Matrix([[1], [1], [1], [1], [1], [1], [1], [1], [1], [1]]))[1, 1]: seq(a(n), n=1..20); # Alois P. Heinz, Aug 28 2008 CROSSREFS Cf. A138977, A138978. Sequence in context: A158645 A348634 A232951 * A183505 A218717 A159234 Adjacent sequences: A138976 A138977 A138978 * A138980 A138981 A138982 KEYWORD nonn AUTHOR Wayne VanWeerthuizen, Apr 05 2008 EXTENSIONS More terms from Alois P. Heinz, Aug 28 2008 STATUS approved

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Last modified November 28 22:51 EST 2022. Contains 358421 sequences. (Running on oeis4.)