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%I #7 Dec 12 2014 20:56:41
%S 8,334,3424,21152,89836,303924,860360,2143214,4811604,9963600,
%T 19277184,35285668,61579724,103227698,167041476,262183860,400496168,
%U 597331512,871946544,1248604446,1757018272,2433781036,3322847752,4477336960
%N Number of length 4+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum
%C Row 4 of A247726
%H R. H. Hardin, <a href="/A247730/b247730.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-2) +2*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -4*a(n-7) -3*a(n-8) -a(n-9) +a(n-10) +4*a(n-11) +6*a(n-12) +5*a(n-13) +2*a(n-14) -2*a(n-15) -6*a(n-16) -6*a(n-17) -6*a(n-18) -2*a(n-19) +2*a(n-20) +5*a(n-21) +6*a(n-22) +4*a(n-23) +a(n-24) -a(n-25) -3*a(n-26) -4*a(n-27) -2*a(n-28) -a(n-29) +2*a(n-30) +2*a(n-31) +a(n-32) -a(n-34)
%F Also a polynomial of degree 7 plus a cubic quasipolynomial with period 420. The first 12 are :
%F Empirical for n mod 420 = 0: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (41057/1260)*n^3 - (13277/420)*n^2 + (137/7)*n
%F Empirical for n mod 420 = 1: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (35387/1260)*n^3 - (8657/420)*n^2 + (1/63)*n + (913/180)
%F Empirical for n mod 420 = 2: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (41057/1260)*n^3 - (37591/1260)*n^2 + (631/63)*n + (2353/315)
%F Empirical for n mod 420 = 3: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (35387/1260)*n^3 - (8657/420)*n^2 - (149/21)*n + (417/20)
%F Empirical for n mod 420 = 4: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (41057/1260)*n^3 - (13277/420)*n^2 + (1681/63)*n - (4136/315)
%F Empirical for n mod 420 = 5: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (35387/1260)*n^3 - (23731/1260)*n^2 - (1301/63)*n + (10547/252)
%F Empirical for n mod 420 = 6: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (41057/1260)*n^3 - (13277/420)*n^2 + (165/7)*n - (369/35)
%F Empirical for n mod 420 = 7: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (35387/1260)*n^3 - (8657/420)*n^2 + (1/63)*n + (1561/180)
%F Empirical for n mod 420 = 8: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (41057/1260)*n^3 - (37591/1260)*n^2 + (379/63)*n + (862/45)
%F Empirical for n mod 420 = 9: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (35387/1260)*n^3 - (8657/420)*n^2 - (149/21)*n + (2319/140)
%F Empirical for n mod 420 = 10: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (41057/1260)*n^3 - (13277/420)*n^2 + (1933/63)*n - (175/9)
%F Empirical for n mod 420 = 11: a(n) = 1*n^7 - 1*n^6 + (653/60)*n^5 - (139/9)*n^4 + (35387/1260)*n^3 - (23731/1260)*n^2 - (1301/63)*n + (62311/1260)
%e Some solutions for n=5
%e ..5....4....3....0....5....2....0....2....0....4....1....2....1....4....1....0
%e ..4....0....5....4....1....2....5....3....4....4....0....2....3....2....3....3
%e ..3....3....5....4....3....5....5....1....0....1....1....0....1....1....2....2
%e ..0....3....2....5....4....3....3....3....0....5....3....1....5....1....5....2
%e ..4....2....0....1....1....3....0....2....1....4....1....5....1....1....2....4
%e ..2....3....5....4....5....0....1....5....3....1....5....3....1....3....1....3
%e ..0....3....2....3....1....1....3....1....3....3....4....4....2....5....3....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 23 2014
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