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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.)