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proposed

Row 6 of A269656.

Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 3*n^2 + 3*n.

Conjectures from Colin Barker, Jan 25 2019: (Start)

G.f.: 2*x*(21 + 166*x + 158*x^2 + 17*x^4 - 2*x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Some solutions for n=3:

Cf. Row 6 of A269656.

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R. H. Hardin, <a href="/A269659/b269659.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of length-6 0..n arrays with no adjacent pair x,x+1 repeated.

42, 626, 3816, 15036, 45590, 115902, 259476, 527576, 994626, 1764330, 2976512, 4814676, 7514286, 11371766, 16754220, 24109872, 33979226, 47006946, 63954456, 85713260, 113318982, 147966126, 191023556, 244050696, 308814450, 387306842

1,1

Row 6 of A269656.

Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 3*n^2 + 3*n

Some solutions for n=3

..1. .3. .3. .1. .2. .0. .1. .2. .2. .0. .3. .2. .2. .0. .2. .2

..1. .0. .3. .0. .2. .0. .1. .3. .2. .0. .2. .0. .1. .3. .1. .0

..1. .2. .0. .0. .2. .2. .2. .0. .0. .0. .0. .3. .0. .2. .0. .2

..2. .0. .1. .3. .2. .0. .3. .1. .2. .2. .1. .3. .0. .2. .2. .0

..1. .0. .2. .0. .0. .3. .0. .1. .0. .2. .0. .1. .1. .0. .1. .1

..3. .1. .2. .1. .2. .2. .0. .1. .3. .0. .2. .3. .2. .0. .2. .3

Cf. A269656.

allocated

nonn

R. H. Hardin, Mar 02 2016

approved

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allocated for R. H. Hardin

allocated

approved