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A247534 Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.

%I A247534 #8 Nov 07 2018 11:29:31
%S A247534 8,45,136,317,600,1033,1616,2409,3400,4661,6168,8005,10136,12657,
%T A247534 15520,18833,22536,26749,31400,36621,42328,48665,55536,63097,71240,
%U A247534 80133,89656,99989,111000,122881,135488,149025,163336,178637,194760,211933,229976
%N A247534 Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.
%H A247534 R. H. Hardin, <a href="/A247534/b247534.txt">Table of n, a(n) for n = 1..210</a>
%F A247534 Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A247534 Also as a cubic plus a linear quasipolynomial with period 2:
%F A247534 Empirical for n mod 2 = 0: a(n) = (9/2)*n^3 + (3/2)*n^2 + 1*n + 1
%F A247534 Empirical for n mod 2 = 1: a(n) = (9/2)*n^3 + (3/2)*n^2 - (1/2)*n + (5/2).
%F A247534 Empirical g.f.: x*(8 + 29*x + 38*x^2 + 32*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2). - _Colin Barker_, Nov 07 2018
%e A247534 Some solutions for n=6:
%e A247534 ..4....0....4....5....6....4....3....3....0....4....3....0....6....5....3....0
%e A247534 ..3....4....4....4....1....2....0....2....5....4....5....1....3....4....1....2
%e A247534 ..3....6....3....2....4....3....3....4....1....5....5....3....2....6....4....0
%e A247534 ..4....2....3....3....3....3....0....3....6....5....3....4....5....5....6....2
%e A247534 ..4....4....4....3....6....4....3....1....2....6....3....6....0....5....3....0
%Y A247534 Row 2 of A247533.
%K A247534 nonn
%O A247534 1,1
%A A247534 _R. H. Hardin_, Sep 18 2014