cp's OEIS Frontend

A245951 Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

%I A245951 #8 Nov 05 2018 07:59:51
%S A245951 14,71,196,453,834,1435,2216,3305,4630,6351,8364,10861,13706,17123,
%T A245951 20944,25425,30366,36055,42260,49301,56914,65451,74616,84793,95654,
%U A245951 107615,120316,134205,148890,164851,181664,199841,218926,239463,260964,284005
%N A245951 Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.
%H A245951 R. H. Hardin, <a href="/A245951/b245951.txt">Table of n, a(n) for n = 1..210</a>
%F A245951 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 A245951 Conjectures from _Colin Barker_, Nov 05 2018: (Start)
%F A245951 G.f.: x*(14 + 43*x + 40*x^2 + 46*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
%F A245951 a(n) = 1 + 5*n + 3*n^2 + 6*n^3 for n even.
%F A245951 a(n) = 4 + n + 3*n^2 + 6*n^3 for n odd.
%F A245951 (End)
%e A245951 Some solutions for n=10:
%e A245951 ..6....5....7...10....6....7....6....0....3....6....1....8....5....1...10....8
%e A245951 ..5....7....5....1...10...10....9...10....7....5...10...10....5....5....9....2
%e A245951 ..3....6...10....9....4....6....6....8....7....4....9....4....2....5....7....1
%e A245951 ..7....4....5....7...10....4....1...10....7....6....5....0....0....2....0....6
%Y A245951 Row 1 of A245950.
%K A245951 nonn
%O A245951 1,1
%A A245951 _R. H. Hardin_, Aug 08 2014