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 A202965 Number of arrays of 5 integers in -n..n with sum zero and adjacent elements differing in absolute value. 1

%I

%S 2,82,414,1562,4048,9010,17296,30648,50232,78388,116614,167824,233858,

%T 318234,423094,552554,709104,897434,1120360,1383176,1689016,2043772,

%U 2450910,2916896,3445538,4043906,4716110,5469818,6309488,7243362,8276224

%N Number of arrays of 5 integers in -n..n with sum zero and adjacent elements differing in absolute value.

%C Row 3 of A202962.

%H R. H. Hardin, <a href="/A202965/b202965.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11).

%F Empirical g.f.: 2*x*(1 + 39*x + 125*x^2 + 368*x^3 + 503*x^4 + 666*x^5 + 499*x^6 + 384*x^7 + 120*x^8 + 55*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jun 03 2018

%e Some solutions for n=5:

%e ..0....5....5....5...-5....2...-4...-1...-3....3....2...-2...-5....0...-1...-2

%e .-2....0....2...-2...-2....0....3...-5...-5...-4...-1....5....0...-4....2....5

%e ..0...-1...-5...-4....4...-4....4...-1....1...-3...-3...-4....2....5....1...-1

%e ..2....0...-2....1....2...-2...-2....2....4....4....0...-1....4....4....3....0

%e ..0...-4....0....0....1....4...-1....5....3....0....2....2...-1...-5...-5...-2

%Y Cf. A202962.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2011

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Last modified May 18 18:42 EDT 2022. Contains 353824 sequences. (Running on oeis4.)