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A249987 Number of length 7+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 7*n.

%I A249987 #6 Jul 23 2025 12:09:27
%S A249987 1012,31380,245860,1293326,4598532,14027522,35380112,82176822,
%T A249987 170479400,335836428,613774848,1082535196,1809905436,2948384694,
%U A249987 4614428112,7080133636,10530399420,15419165316,22022418940,31058475666,42919172164
%N A249987 Number of length 7+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 7*n.
%C A249987 Row 7 of A249982
%H A249987 R. H. Hardin, <a href="/A249987/b249987.txt">Table of n, a(n) for n = 1..210</a>
%F A249987 Empirical: a(n) = 2*a(n-1) +5*a(n-2) -12*a(n-3) -9*a(n-4) +30*a(n-5) +5*a(n-6) -40*a(n-7) +5*a(n-8) +30*a(n-9) -9*a(n-10) -12*a(n-11) +5*a(n-12) +2*a(n-13) -a(n-14)
%F A249987 Empirical for n mod 2 = 0: a(n) = (459901/26880)*n^7 + (238219/1920)*n^6 + (682979/1920)*n^5 + (30971/64)*n^4 + (124069/480)*n^3 + (337/240)*n^2 + (10541/420)*n
%F A249987 Empirical for n mod 2 = 1: a(n) = (459901/26880)*n^7 + (238219/1920)*n^6 + (86757/256)*n^5 + (50735/128)*n^4 + (513337/3840)*n^3 - (25939/1920)*n^2 + (87707/5376)*n - (119/128)
%e A249987 Some solutions for n=2
%e A249987 ..0....2....2....1....1....4....0....1....0....0....3....0....2....2....1....2
%e A249987 ..4....2....3....3....2....3....0....4....4....1....0....3....4....4....4....0
%e A249987 ..1....0....3....4....1....1....4....1....0....1....2....1....0....4....0....2
%e A249987 ..0....0....0....2....4....2....0....4....1....0....0....1....0....2....3....2
%e A249987 ..3....4....4....0....0....4....2....1....3....3....4....4....4....4....2....4
%e A249987 ..3....3....3....3....2....1....0....2....1....0....3....1....2....0....3....0
%e A249987 ..1....0....1....0....3....0....1....3....1....3....2....0....3....2....2....3
%e A249987 ..0....4....4....1....1....4....0....3....0....0....3....2....4....0....1....4
%K A249987 nonn
%O A249987 1,1
%A A249987 _R. H. Hardin_, Nov 10 2014