cp's OEIS Frontend

A250229 T(n,k)=Number of length n+1 0..k arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.

%I A250229 #10 Jun 19 2020 04:02:14
%S A250229 2,3,4,4,11,8,5,20,27,16,6,33,52,79,32,7,48,89,208,223,64,8,67,132,
%T A250229 473,704,651,128,9,88,187,872,1785,2720,1907,256,10,113,248,1519,3496,
%U A250229 9437,10952,5639,512,11,140,321,2392,6367,24888,47953,45888,16967,1024,12,171
%N A250229 T(n,k)=Number of length n+1 0..k arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.
%H A250229 R. H. Hardin, <a href="/A250229/b250229.txt">Table of n, a(n) for n = 1..181</a>
%F A250229 Empirical for column k:
%F A250229 k=1: a(n) = 2*a(n-1)
%F A250229 k=2: [linear recurrence of order 9] for n>12
%F A250229 Empirical for row n:
%F A250229 n=1: a(n) = n + 1
%F A250229 n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2
%F A250229 n=3: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2
%e A250229 Table starts
%e A250229 ....2.....3......4.......5........6.........7.........8..........9.........10
%e A250229 ....4....11.....20......33.......48........67........88........113........140
%e A250229 ....8....27.....52......89......132.......187.......248........321........400
%e A250229 ...16....79....208.....473......872......1519......2392.......3617.......5184
%e A250229 ...32...223....704....1785.....3496......6367.....10640......16909......25152
%e A250229 ...64...651...2720....9437....24888.....59415....120412.....222037.....374712
%e A250229 ..128..1907..10952...47953...144624....371227....838604....1732385....3243544
%e A250229 ..256..5639..45888..264473..1019568...3347259...8983896...21295973...45095084
%e A250229 ..512.16967.195516.1440243..6717892..25280899..78435176..215244983..519836920
%e A250229 .1024.52131.852260.8079297.47046932.217539879.789142896.2486304965.6802360404
%e A250229 ...
%e A250229 Some solutions for n=6 k=4
%e A250229 ..4....2....2....2....3....2....0....2....2....2....1....3....1....2....2....4
%e A250229 ..3....1....1....3....0....3....2....1....0....0....4....0....0....4....1....0
%e A250229 ..1....0....3....2....2....3....3....4....0....4....1....1....0....3....1....4
%e A250229 ..3....3....1....1....0....1....3....1....2....0....3....0....3....3....0....2
%e A250229 ..0....1....2....0....0....0....3....3....4....2....2....3....4....2....2....0
%e A250229 ..3....4....1....3....3....2....1....4....2....4....0....0....4....2....2....3
%e A250229 ..2....2....0....0....3....2....2....2....2....2....1....3....1....0....4....0
%Y A250229 Column 1 is A000079.
%Y A250229 Row 2 is A212959.
%K A250229 nonn,tabl
%O A250229 1,1
%A A250229 _R. H. Hardin_, Nov 14 2014