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A269660 Number of length-7 0..n arrays with no adjacent pair x,x+1 repeated. 2

%I #8 Jan 26 2019 05:02:47

%S 64,1710,14596,73348,269472,803434,2061940,4725456,9911008,19355302,

%T 35643204,62486620,105058816,170389218,267823732,409555624,611232000,

%U 892640926,1278484228,1799241012,2492126944,3402154330,4583298036

%N Number of length-7 0..n arrays with no adjacent pair x,x+1 repeated.

%H R. H. Hardin, <a href="/A269660/b269660.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + 7*n^6 + 21*n^5 + 25*n^4 + 5*n^3 + 2*n^2 + 11*n - 8.

%F Conjectures from _Colin Barker_, Jan 26 2019: (Start)

%F G.f.: 2*x*(32 + 599*x + 1354*x^2 + 438*x^3 + 48*x^4 + 71*x^5 - 26*x^6 + 4*x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=3:

%e ..1. .1. .0. .0. .2. .0. .0. .2. .0. .1. .0. .1. .2. .0. .1. .2

%e ..3. .1. .0. .1. .0. .3. .3. .0. .0. .0. .1. .2. .0. .3. .3. .2

%e ..0. .0. .2. .2. .1. .1. .0. .1. .2. .2. .3. .3. .3. .3. .1. .2

%e ..1. .3. .0. .0. .0. .3. .1. .0. .3. .3. .0. .1. .2. .0. .1. .1

%e ..2. .0. .1. .0. .3. .2. .1. .2. .0. .2. .0. .0. .1. .0. .3. .3

%e ..0. .2. .2. .2. .3. .0. .2. .2. .3. .2. .0. .0. .2. .3. .0. .3

%e ..3. .3. .1. .2. .1. .3. .1. .1. .2. .2. .0. .2. .2. .3. .3. .2

%Y Row 7 of A269656.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2016

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)