cp's OEIS Frontend

A246894 Number of length 2+4 0..n arrays with some pair in every consecutive five terms totalling exactly n.

%I A246894 #8 Nov 07 2018 09:56:55
%S A246894 58,673,3364,12481,33294,79345,159688,303169,521890,866881,1351788,
%T A246894 2057473,2996854,4289041,5943184,8125825,10838538,14305249,18515380,
%U A246894 23760961,30013918,37645873,46605144,57355201,69813874,84549505
%N A246894 Number of length 2+4 0..n arrays with some pair in every consecutive five terms totalling exactly n.
%H A246894 R. H. Hardin, <a href="/A246894/b246894.txt">Table of n, a(n) for n = 1..210</a>
%F A246894 Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).
%F A246894 Conjectures from _Colin Barker_, Nov 07 2018: (Start)
%F A246894 G.f.: x*(58 + 557*x + 1844*x^2 + 4198*x^3 + 3740*x^4 + 2876*x^5 - 268*x^6 - 1486*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).
%F A246894 a(n) = 1 - 72*n + 146*n^2 - 57*n^3 + 31*n^4 + 6*n^5 for n even.
%F A246894 a(n) = -101 + 84*n + 99*n^2 - 61*n^3 + 31*n^4 + 6*n^5 for n odd.
%F A246894 (End)
%e A246894 Some solutions for n=6:
%e A246894 ..4....4....0....0....5....2....5....4....0....2....4....4....5....4....4....3
%e A246894 ..2....4....3....0....5....3....3....5....6....3....6....0....5....2....4....6
%e A246894 ..4....5....4....3....2....4....2....0....6....5....1....1....4....3....6....5
%e A246894 ..2....0....3....6....5....2....3....0....3....5....2....0....1....2....5....1
%e A246894 ..6....1....6....2....1....2....4....1....3....1....4....5....0....1....2....3
%e A246894 ..0....1....4....4....5....4....3....3....3....1....5....6....1....4....0....4
%Y A246894 Row 2 of A246892.
%K A246894 nonn
%O A246894 1,1
%A A246894 _R. H. Hardin_, Sep 06 2014