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A138977
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Number of 2 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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7
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3, 19, 121, 771, 4913, 31307, 199497, 1271251, 8100769, 51620379, 328939577, 2096095523, 13356910353, 85113990379, 542370291241, 3456136077171, 22023471375233, 140339755317947, 894284401724697, 5698631790801091, 36313284928708849, 231398467337757579
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OFFSET
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1,1
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COMMENTS
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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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LINKS
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FORMULA
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a(n)=b(n)+c(n), where b(1)=2, c(1)=1, b(n+1)=4*b(n)+4*c(n), c(n+1)=2*b(n)+3*c(n).
a(n+2) = 7*a(n+1) - 4*a(n) for n >= 2. - Robert Israel, Sep 02 2014
a(n) = (2^(-2-n)*((7-sqrt(33))^n*(-5+sqrt(33)) + (5+sqrt(33))*(7+sqrt(33))^n)) / sqrt(33). - Colin Barker, Jan 31 2018
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EXAMPLE
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a(1) = 3:
|1|1|1|
|0|1|2|
a(2) = 19:
|10|11|12| |10|11|12| |10|11|12|
|0*|0*|01| |1*|1*|1*| |21|2*|2*|
(3) (2)(1) (2) (3)(2) (1) (2)(3), total 19.
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MAPLE
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a:= LREtools[REtoproc](a(n+3)=7*a(n+2)-4*a(n+1), a(n), {a(0)=0, a(1)=3, a(2)=19}):
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MATHEMATICA
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PROG
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(PARI) Vec(x*(3 - 2*x) / (1 - 7*x + 4*x^2) + O(x^30)) \\ Colin Barker, Jan 31 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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