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

8, 105, 604, 1823, 4228, 8051, 13668, 21609, 31924, 45309, 61740, 82067, 105968, 134635, 167680, 206001, 249072, 298861, 354032, 416027, 484464, 560643, 643428, 735401, 834308, 942581, 1059436, 1186239, 1321332, 1468271, 1624036, 1791277

Offset

1,1

Comments

Row 5 of A247533

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

Example

Some solutions for n=6
..3....6....4....4....3....2....5....5....4....1....3....2....5....2....5....6
..1....2....2....3....2....1....6....4....0....2....2....6....6....2....4....4
..2....1....3....4....4....5....0....6....6....5....4....3....3....1....4....5
..0....5....1....3....1....6....1....5....2....4....3....5....2....1....5....3
..1....4....0....2....5....2....5....5....4....3....3....2....5....0....3....4
..3....0....4....1....0....1....4....4....0....6....2....4....6....2....4....2
..4....1....5....0....4....5....2....4....6....5....4....3....1....3....4....3
..6....5....1....3....1....6....3....5....2....2....3....1....0....5....3....3

Crossrefs

Sequence in context: A146346 A285745 A119934 * A302261 A302961 A302804

Adjacent sequences: A247534 A247535 A247536 * A247538 A247539 A247540

Keyword

nonn

Author

R. H. Hardin, Sep 18 2014

Status

approved