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 A201046 Number of -n..n arrays of 7 elements with adjacent element differences also in -n..n. 1

%I #9 May 22 2018 03:47:32

%S 577,17981,182349,1042167,4211559,13497523,36644243,87831605,

%T 191065045,384593857,726495089,1301560155,2229621291,3675454983,

%U 5860399495,9075823625,13698583817,20208606757,29208734581,41446969823,57841257231

%N Number of -n..n arrays of 7 elements with adjacent element differences also in -n..n.

%C Row 7 of A201042.

%H R. H. Hardin, <a href="/A201046/b201046.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (17141/630)*n^7 + (17141/180)*n^6 + (28177/180)*n^5 + (2759/18)*n^4 + (17299/180)*n^3 + (6929/180)*n^2 + (1921/210)*n + 1.

%F Conjectures from _Colin Barker_, May 22 2018: (Start)

%F G.f.: x*(577 + 13365*x + 54657*x^2 + 54531*x^3 + 13449*x^4 + 541*x^5 + 9*x^6 - x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=2:

%e ..1...-1....0....1....2....2....0....0...-2....1...-1....0....2...-2....0....1

%e ..0...-2....0....1....0....2....2....1...-2....2....1....0....2...-1...-1....0

%e ..0....0....0....2...-2....2....0....1....0....0....1...-1....2....1...-1...-2

%e ..0....2...-1....1...-1....0...-1....0....0....0....1....0....2....2...-2...-1

%e .-1....2....0....1....1...-1...-1...-1....2....2....2....1....1....0....0....0

%e .-2....2....0....1....0....1....1...-2....0....0....1....1....1....1....2....0

%e .-2....2....1....1...-1...-1...-1...-1....2...-2...-1...-1...-1....2....2...-2

%Y Cf. A201042.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2011

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Last modified February 29 20:48 EST 2024. Contains 370428 sequences. (Running on oeis4.)