A247730 Number of length 4+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum

8, 334, 3424, 21152, 89836, 303924, 860360, 2143214, 4811604, 9963600, 19277184, 35285668, 61579724, 103227698, 167041476, 262183860, 400496168, 597331512, 871946544, 1248604446, 1757018272, 2433781036, 3322847752, 4477336960

Offset

1,1

Comments

Row 4 of A247726

Links

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

Formula

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)

Also a polynomial of degree 7 plus a cubic quasipolynomial with period 420. The first 12 are :

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Example

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

Crossrefs

Sequence in context: A204069 A226551 A285370 * A258745 A071306 A214511

Adjacent sequences: A247727 A247728 A247729 * A247731 A247732 A247733

Keyword

nonn

Author

R. H. Hardin, Sep 23 2014

Status

approved