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A249320 Number of length 1+6 0..n arrays with no seven consecutive terms having six times any element equal to the sum of the remaining six. 1
126, 1792, 14336, 68712, 249088, 739284, 1898582, 4361056, 9176664, 17982930, 33230442, 58450770, 98581896, 160353634, 252737912, 387464994, 579621658, 848320494, 1217462624, 1716582952, 2381796186, 3256837500, 4394213292 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 1 of A249319.
LINKS
FORMULA
Empirical: a(n) = 6*a(n-1) -16*a(n-2) +26*a(n-3) -30*a(n-4) +27*a(n-5) -21*a(n-6) +16*a(n-7) -11*a(n-8) +4*a(n-9) +4*a(n-10) -11*a(n-11) +16*a(n-12) -21*a(n-13) +27*a(n-14) -30*a(n-15) +26*a(n-16) -16*a(n-17) +6*a(n-18) -a(n-19).
Also a polynomial of degree 7 plus a degree 0 quasipolynomial with period 60; the first 12 are:
Empirical for n mod 60 = 0: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n.
Empirical for n mod 60 = 1: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (1043/60).
Empirical for n mod 60 = 2: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (462/5).
Empirical for n mod 60 = 3: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (1393/20).
Empirical for n mod 60 = 4: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (952/15).
Empirical for n mod 60 = 5: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (357/4).
Empirical for n mod 60 = 6: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (546/5).
Empirical for n mod 60 = 7: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (7931/60).
Empirical for n mod 60 = 8: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (1008/5).
Empirical for n mod 60 = 9: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (3129/20).
Empirical for n mod 60 = 10: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (140/3).
Empirical for n mod 60 = 11: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (1799/20).
EXAMPLE
Some solutions for n=4
..3....4....1....3....3....1....4....0....1....0....3....2....4....1....4....4
..0....4....2....2....0....2....0....1....0....3....1....4....0....1....2....3
..1....4....4....1....4....1....4....3....3....0....3....2....0....0....2....4
..3....1....3....2....2....2....3....4....2....4....2....1....1....0....0....1
..3....3....1....4....2....4....3....1....1....2....0....4....3....0....0....4
..1....3....0....4....1....1....2....4....4....0....3....0....2....2....2....1
..0....3....4....2....3....0....2....1....2....2....3....0....2....0....1....2
CROSSREFS
Cf. A249319.
Sequence in context: A249319 A249198 A249213 * A267628 A304559 A189345
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 25 2014
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)