cp's OEIS Frontend

A228220 Number of second differences of arrays of length 5 of numbers in 0..n.

%I A228220 #7 Sep 10 2018 05:36:34
%S A228220 31,199,625,1429,2731,4651,7309,10825,15319,20911,27721,35869,45475,
%T A228220 56659,69541,84241,100879,119575,140449,163621,189211,217339,248125,
%U A228220 281689,318151,357631,400249,446125,495379,548131,604501,664609,728575
%N A228220 Number of second differences of arrays of length 5 of numbers in 0..n.
%H A228220 R. H. Hardin, <a href="/A228220/b228220.txt">Table of n, a(n) for n = 1..210</a>
%F A228220 Empirical: a(n) = 20*n^3 + 9*n^2 + 1*n + 1.
%F A228220 Conjectures from _Colin Barker_, Sep 10 2018: (Start)
%F A228220 G.f.: x*(31 + 75*x + 15*x^2 - x^3) / (1 - x)^4.
%F A228220 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A228220 (End)
%e A228220 Some solutions for n=4:
%e A228220 .-2....1...-5....4....0....1....1....3...-2....4...-5...-8....4...-4....0....3
%e A228220 .-2...-2....6....0....2...-3....4....0....5....3....7....7...-6...-4....1...-7
%e A228220 .-2....5....0...-2...-5....7...-7...-2...-3...-6...-2...-2....3....4...-3....4
%Y A228220 Row 3 of A228218.
%K A228220 nonn
%O A228220 1,1
%A A228220 _R. H. Hardin_, Aug 16 2013