%I #6 May 27 2012 07:28:31
%S 21,397,4379,22972,91482,284360,764297,1797975,3883755,7729696,
%T 14517156,25811656,44024953,72163603,114677011,176842932,266174946,
%U 391374778,564396617,798717009,1112552471,1525915970,2065331568,2759616340
%N Half the number of 0..n arrays of length 7 with second differences nonzero
%C Row 5 of A212782
%H R. H. Hardin, <a href="/A212786/b212786.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = -a(n-1) -a(n-2) +a(n-3) +4*a(n-4) +6*a(n-5) +7*a(n-6) +a(n-7) -6*a(n-8) -16*a(n-9) -20*a(n-10) -16*a(n-11) -2*a(n-12) +18*a(n-13) +32*a(n-14) +38*a(n-15) +24*a(n-16) +2*a(n-17) -27*a(n-18) -43*a(n-19) -43*a(n-20) -27*a(n-21) +2*a(n-22) +24*a(n-23) +38*a(n-24) +32*a(n-25) +18*a(n-26) -2*a(n-27) -16*a(n-28) -20*a(n-29) -16*a(n-30) -6*a(n-31) +a(n-32) +7*a(n-33) +6*a(n-34) +4*a(n-35) +a(n-36) -a(n-37) -a(n-38) -a(n-39)
%e Some solutions for n=5
%e ..3....1....0....1....3....3....1....0....1....0....4....3....0....1....4....0
%e ..3....1....0....4....5....2....0....5....3....1....0....1....1....1....4....5
%e ..5....0....4....2....1....2....2....3....3....5....1....3....5....5....0....2
%e ..1....1....3....1....2....4....2....2....1....3....4....0....4....1....1....3
%e ..5....0....0....5....1....0....5....4....3....4....4....4....1....2....1....5
%e ..1....4....4....4....2....0....5....3....4....0....3....2....0....4....5....0
%e ..4....4....3....1....0....5....1....5....1....0....5....5....0....0....2....1
%K nonn
%O 1,1
%A _R. H. Hardin_ May 27 2012