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A247537 Number of length 5+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum 1

%I

%S 8,105,604,1823,4228,8051,13668,21609,31924,45309,61740,82067,105968,

%T 134635,167680,206001,249072,298861,354032,416027,484464,560643,

%U 643428,735401,834308,942581,1059436,1186239,1321332,1468271,1624036,1791277

%N Number of length 5+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum

%C Row 5 of A247533

%H R. H. Hardin, <a href="/A247537/b247537.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = -3*a(n-1) -6*a(n-2) -10*a(n-3) -15*a(n-4) -19*a(n-5) -21*a(n-6) -20*a(n-7) -15*a(n-8) -5*a(n-9) +9*a(n-10) +26*a(n-11) +44*a(n-12) +60*a(n-13) +71*a(n-14) +75*a(n-15) +70*a(n-16) +55*a(n-17) +32*a(n-18) +3*a(n-19) -29*a(n-20) -60*a(n-21) -85*a(n-22) -102*a(n-23) -108*a(n-24) -102*a(n-25) -85*a(n-26) -60*a(n-27) -29*a(n-28) +3*a(n-29) +32*a(n-30) +55*a(n-31) +70*a(n-32) +75*a(n-33) +71*a(n-34) +60*a(n-35) +44*a(n-36) +26*a(n-37) +9*a(n-38) -5*a(n-39) -15*a(n-40) -20*a(n-41) -21*a(n-42) -19*a(n-43) -15*a(n-44) -10*a(n-45) -6*a(n-46) -3*a(n-47) -a(n-48)

%F Also as a cubic plus a linear quasipolynomial with period 27720, first 12 listed:

%F Empirical for n mod 27720 = 0: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (878029/6930)*n + 1

%F Empirical for n mod 27720 = 1: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (3587189/34650)*n - (44311/13860)

%F Empirical for n mod 27720 = 2: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (420821/3850)*n + (45853/2475)

%F Empirical for n mod 27720 = 3: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (716329/6930)*n + (17263/300)

%F Empirical for n mod 27720 = 4: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (4379057/34650)*n - (891203/17325)

%F Empirical for n mod 27720 = 5: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (198223/2310)*n + (44759/252)

%F Empirical for n mod 27720 = 6: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (4395689/34650)*n - (68743/1155)

%F Empirical for n mod 27720 = 7: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (3587189/34650)*n + (341887/9900)

%F Empirical for n mod 27720 = 8: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (84041/770)*n + (1394257/17325)

%F Empirical for n mod 27720 = 9: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (3570557/34650)*n + (56851/1100)

%F Empirical for n mod 27720 = 10: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (878029/6930)*n - (9023/99)

%F Empirical for n mod 27720 = 11: a(n) = (1027297/17325)*n^3 - (3502537/23100)*n^2 + (992963/11550)*n + (275239/1260)

%e Some solutions for n=6

%e ..3....6....4....4....3....2....5....5....4....1....3....2....5....2....5....6

%e ..1....2....2....3....2....1....6....4....0....2....2....6....6....2....4....4

%e ..2....1....3....4....4....5....0....6....6....5....4....3....3....1....4....5

%e ..0....5....1....3....1....6....1....5....2....4....3....5....2....1....5....3

%e ..1....4....0....2....5....2....5....5....4....3....3....2....5....0....3....4

%e ..3....0....4....1....0....1....4....4....0....6....2....4....6....2....4....2

%e ..4....1....5....0....4....5....2....4....6....5....4....3....1....3....4....3

%e ..6....5....1....3....1....6....3....5....2....2....3....1....0....5....3....3

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 18 2014

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)