A250556 - OEIS

A250556

Number of length n+2 0..3 arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero.

%I #20 Mar 07 2023 04:26:11

%S 8,60,302,1516,7126,30780,127586,518052,2085808,8367220,33513408,

%T 134137736,536713774,2147172564,8589316642,34358507208,137436497326,

%U 549750908948,2199013454674,8796073430888,35184332920270,140737410034420

%N Number of length n+2 0..3 arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero.

%C Column 3 of A250561.

%H Manuel Kauers and Christoph Koutschan, <a href="/A250556/b250556.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..47 from R. H. Hardin).

%H M. Kauers and C. Koutschan, <a href="https://arxiv.org/abs/2303.02793">Some D-finite and some possibly D-finite sequences in the OEIS</a>, arXiv:2303.02793 [cs.SC], 2023.

%F From _Manuel Kauers_ and _Christoph Koutschan_, Mar 01 2023: (Start)

%F Generating function: 2*x*(4 + 2*x - 3*x^2 + 73*x^3 + 115*x^4 - 139*x^5 - 453*x^6 - 1231*x^7 + 38*x^8 + 406*x^9 + 3597*x^10 + 2087*x^11 + 1666*x^12 - 3614*x^13 - 4178*x^14 - 4504*x^15 + 903*x^16 + 1985*x^17 + 4173*x^18 + 403*x^19 - 202*x^20 - 1324*x^21 - 1296*x^22 + 684*x^23 - 300*x^24 + 508*x^25 - 56*x^26 + 32*x^27)/((1 - 4*x)*(1 - 2*x)*(1 - x)^3*(1 + x)^2*(1 + x^2)^2*(1 - 2*x^3)^2).

%F Recurrence equation: 32*a(n) - 56*a(n + 1) + 28*a(n + 2) - 36*a(n + 3) - 8*a(n + 4) + 84*a(n + 5) - 44*a(n + 6) + 58*a(n + 7) - 73*a(n + 8) - a(n + 9) + 4*a(n + 10) - 8*a(n + 11) + 42*a(n + 12) - 26*a(n + 13) + 12*a(n + 14) - 14*a(n + 15) + 7*a(n + 16) - a(n + 17) = 0 for n>11. (End)

%e Some solutions for n=6

%e 3 1 1 0 3 3 3 1 1 1 3 0 1 2 0 2

%e 2 2 0 0 0 3 0 0 0 2 3 3 1 2 1 2

%e 3 2 2 1 2 1 0 2 1 2 2 2 3 1 1 2

%e 2 2 2 3 0 1 0 3 1 2 0 1 3 3 3 0

%e 1 0 1 2 1 3 1 3 2 2 0 2 1 3 1 1

%e 0 3 0 1 1 2 3 3 0 2 0 1 3 3 0 2

%e 3 1 2 0 3 3 3 0 2 1 3 1 0 0 3 2

%e 2 0 3 0 0 1 0 3 1 2 3 2 2 0 0 2

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 25 2014