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Search: id:A138978
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| A138978 |
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Number of 3 X n matrices containing a 1 in the top left entry, all entries are integer values and adjacent entries differ by at most 1. |
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+0
3
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| 9, 121, 1665, 22979, 317259, 4380445, 60481881, 835088891, 11530288395, 159201677509, 2198138788809, 30350271502115, 419054058355851, 5785987905016141, 79888633386248025, 1103043049708026539
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Horizontally or vertically adjacent entries can differ by at most 1. Diagonally adjacent entries thus differ by at most 2.
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FORMULA
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a(n)=b(n)+c(n)+d(n), where b(1)=1, c(1)=6, d(1)=2,
b(n+1)=3*b(n)+2*c(n)+1*d(n)
c(n+1)=12*b(n)+10*c(n)+6*d(n)
d(n+1)=2*b(n)+2*c(n)+3*d(n)
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MAPLE
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a:= n-> (Matrix([1, 6, 2]). Matrix([[3, 12, 2], [2, 10, 2], [1, 6, 3]])^(n-1) .Matrix([[1], [1], [1]]))[1, 1]: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 28 2008]
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CROSSREFS
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Cf. A138977, A138979.
Sequence in context: A017102 A167722 A103930 this_sequence A046184 A084769 A050353
Adjacent sequences: A138975 A138976 A138977 this_sequence A138979 A138980 A138981
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KEYWORD
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nonn,easy
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AUTHOR
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Wayne VanWeerthuizen (sequences(AT)waynemv.net), Apr 05 2008
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 28 2008
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