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 A224574 Number of (n+5) X 10 0..1 matrices with each 6 X 6 subblock idempotent. 1

%I #8 Sep 01 2018 12:36:51

%S 22096,7034,7295,8143,8880,9480,9946,11672,14594,18457,22982,27995,

%T 33345,40295,50032,63512,81392,104167,132157,166965,211369,269127,

%U 344634,442792,568799,729476,934410,1196970,1534900,1970858,2532676,3255027

%N Number of (n+5) X 10 0..1 matrices with each 6 X 6 subblock idempotent.

%C Column 5 of A224577.

%H R. H. Hardin, <a href="/A224574/b224574.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 3*a(n-3) + 3*a(n-4) - 6*a(n-5) + 5*a(n-6) - 4*a(n-7) + 3*a(n-8) - 3*a(n-10) + 3*a(n-11) - a(n-12) for n>16.

%F Empirical g.f.: x*(22096 - 81350*x + 111735*x^2 - 45121*x^3 - 67312*x^4 + 112407*x^5 - 89284*x^6 + 74683*x^7 - 53267*x^8 - 7522*x^9 + 61319*x^10 - 53808*x^11 + 14565*x^12 + 694*x^13 + 119*x^14 + 44*x^15) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 - x - x^6)). - _Colin Barker_, Sep 01 2018

%e Some solutions for n=2:

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

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

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

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

%e ..0..0..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0..0..0

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

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

%Y Cf. A224577.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013

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Last modified February 29 02:52 EST 2024. Contains 370401 sequences. (Running on oeis4.)