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A247730 Number of length 4+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum 1
8, 334, 3424, 21152, 89836, 303924, 860360, 2143214, 4811604, 9963600, 19277184, 35285668, 61579724, 103227698, 167041476, 262183860, 400496168, 597331512, 871946544, 1248604446, 1757018272, 2433781036, 3322847752, 4477336960 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)