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A202659 Number of -3..3 arrays of n elements with first through fourth differences also in -3..3.

%I A202659 #7 Jun 02 2025 07:26:19
%S A202659 7,37,153,475,1101,2591,6055,14199,33289,78119,183447,430889,1011945,
%T A202659 2376423,5580971,13107163,30782605,72293525,169783471,398743229,
%U A202659 936465399,2199327501,5165208441,12130703729,28489466517,66908707817
%N A202659 Number of -3..3 arrays of n elements with first through fourth differences also in -3..3.
%C A202659 Column 3 of A202664
%H A202659 R. H. Hardin, <a href="/A202659/b202659.txt">Table of n, a(n) for n = 1..210</a>
%F A202659 Empirical: a(n) = 5*a(n-1) -10*a(n-2) +15*a(n-3) -23*a(n-4) +35*a(n-5) -55*a(n-6) +70*a(n-7) -79*a(n-8) +92*a(n-9) -121*a(n-10) +134*a(n-11) -75*a(n-12) +57*a(n-13) -59*a(n-14) +38*a(n-15) +79*a(n-16) -242*a(n-17) +321*a(n-18) -392*a(n-19) +418*a(n-20) -695*a(n-21) +682*a(n-22) -386*a(n-23) +129*a(n-24) +79*a(n-25) -185*a(n-26) +488*a(n-27) -496*a(n-28) +728*a(n-29) -84*a(n-30) -854*a(n-31) +552*a(n-32) -973*a(n-33) +1092*a(n-34) -551*a(n-35) +798*a(n-36) -267*a(n-37) -405*a(n-38) +245*a(n-39) -403*a(n-40) +342*a(n-41) -135*a(n-42) +183*a(n-43) -36*a(n-44) -108*a(n-45) -23*a(n-46) +44*a(n-47) +45*a(n-48) +95*a(n-49) +34*a(n-50) -7*a(n-51) -66*a(n-52) -24*a(n-53) -52*a(n-54) +27*a(n-55) -7*a(n-56) -13*a(n-57) -14*a(n-58) -2*a(n-59) +13*a(n-60) +3*a(n-61) +a(n-62) +3*a(n-63) +a(n-64) -3*a(n-66) -a(n-68) -a(n-69) for n>78
%e A202659 Some solutions for n=10
%e A202659 ..2...-2....1....1....2...-3...-2....0....1...-3...-2....0...-1....2...-2...-3
%e A202659 .-1...-2....3....0....2...-1....0...-1...-1...-3...-1....1....1...-1....1...-1
%e A202659 .-3...-1....2....1....3....1....0....0...-1...-2...-1....1....2...-2....1....0
%e A202659 .-3....0....0....1....3....1...-1....1...-1...-2...-1....2....2...-1....0....0
%e A202659 .-1....0...-1....0....1....0...-3....2...-2...-2....0....3....2....1....0....0
%e A202659 ..1...-1...-1....0...-1...-1...-3....2...-3...-1....0....2....2....2....0....0
%e A202659 ..3...-1...-2....0...-2...-1...-1....1...-3....0...-1....0....2....3...-1....0
%e A202659 ..3....0...-3...-1...-3....0....1...-1...-1....0...-1...-2....1....2...-2...-1
%e A202659 ..1....2...-3...-2...-2....2....2...-1....1....0....0...-2....1....0...-3...-3
%e A202659 .-2....2...-3...-2....0....2....2....2....1....0....3....0....2....0...-3...-3
%K A202659 nonn
%O A202659 1,1
%A A202659 _R. H. Hardin_ Dec 22 2011