cp's OEIS Frontend

A250170 Number of length 5+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

%I A250170 #8 Jul 23 2025 12:14:57
%S A250170 32,373,1880,7109,19896,49037,103556,203615,364900,624811,1006084,
%T A250170 1570791,2347840,3431579,4856212,6757417,9171308,12285541,16134624,
%U A250170 20968689,26816804,34003157,42544984,52855367,64932468,79290519,95903144
%N A250170 Number of length 5+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.
%C A250170 Row 5 of A250167
%H A250170 R. H. Hardin, <a href="/A250170/b250170.txt">Table of n, a(n) for n = 1..66</a>
%F A250170 Empirical: a(n) = a(n-2) +a(n-3) +2*a(n-4) -a(n-6) -3*a(n-7) -3*a(n-8) -a(n-9) +3*a(n-11) +4*a(n-12) +3*a(n-13) -a(n-15) -3*a(n-16) -3*a(n-17) -a(n-18) +2*a(n-20) +a(n-21) +a(n-22) -a(n-24)
%F A250170 Empirical: also a polynomial of degree 5 plus a cubic quasipolynomial with period 60, the first 12 being:
%F A250170 Empirical for n mod 60 = 0: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n + 1
%F A250170 Empirical for n mod 60 = 1: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (223/64)*n + (457247/8640)
%F A250170 Empirical for n mod 60 = 2: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (2339/36)*n + (7721/270)
%F A250170 Empirical for n mod 60 = 3: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (703/64)*n + (7753/64)
%F A250170 Empirical for n mod 60 = 4: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (1141/135)
%F A250170 Empirical for n mod 60 = 5: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (7639/576)*n + (217043/1728)
%F A250170 Empirical for n mod 60 = 6: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (157/10)
%F A250170 Empirical for n mod 60 = 7: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (703/64)*n + (893567/8640)
%F A250170 Empirical for n mod 60 = 8: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (2339/36)*n + (1223/27)
%F A250170 Empirical for n mod 60 = 9: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (223/64)*n + (24653/320)
%F A250170 Empirical for n mod 60 = 10: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (1531/54)
%F A250170 Empirical for n mod 60 = 11: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (11959/576)*n + (1493887/8640)
%e A250170 Some solutions for n=6
%e A250170 ..6....3....3....3....4....6....4....3....5....1....6....4....1....0....6....3
%e A250170 ..3....1....0....1....6....4....3....3....1....5....6....3....4....0....4....5
%e A250170 ..1....6....2....2....5....6....0....2....2....5....4....3....5....3....1....1
%e A250170 ..0....2....4....4....0....0....3....4....3....4....0....2....3....1....2....1
%e A250170 ..5....1....1....6....2....0....5....2....1....3....4....1....4....2....6....1
%e A250170 ..6....1....5....3....2....6....6....3....1....5....6....2....3....0....6....3
%K A250170 nonn
%O A250170 1,1
%A A250170 _R. H. Hardin_, Nov 13 2014