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
Keywords
Examples
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
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)
Comments