login
Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.
1

%I #8 Nov 07 2018 11:29:31

%S 8,45,136,317,600,1033,1616,2409,3400,4661,6168,8005,10136,12657,

%T 15520,18833,22536,26749,31400,36621,42328,48665,55536,63097,71240,

%U 80133,89656,99989,111000,122881,135488,149025,163336,178637,194760,211933,229976

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

%H R. H. Hardin, <a href="/A247534/b247534.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Also as a cubic plus a linear quasipolynomial with period 2:

%F Empirical for n mod 2 = 0: a(n) = (9/2)*n^3 + (3/2)*n^2 + 1*n + 1

%F Empirical for n mod 2 = 1: a(n) = (9/2)*n^3 + (3/2)*n^2 - (1/2)*n + (5/2).

%F 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 Some solutions for n=6:

%e ..4....0....4....5....6....4....3....3....0....4....3....0....6....5....3....0

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

%e ..3....6....3....2....4....3....3....4....1....5....5....3....2....6....4....0

%e ..4....2....3....3....3....3....0....3....6....5....3....4....5....5....6....2

%e ..4....4....4....3....6....4....3....1....2....6....3....6....0....5....3....0

%Y Row 2 of A247533.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 18 2014