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 A224562 Number of (n+3) X 5 0..1 matrices with each 4 X 4 subblock idempotent. 1

%I

%S 370,340,428,517,611,775,1044,1383,1808,2373,3190,4323,5868,7946,

%T 10825,14809,20317,27872,38285,52646,72495,99863,137615,189693,261595,

%U 360821,497771,686759,947616,1307656,1804613,2490510,3437232,4743946,6547576

%N Number of (n+3) X 5 0..1 matrices with each 4 X 4 subblock idempotent.

%C Column 2 of A224568.

%H R. H. Hardin, <a href="/A224562/b224562.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) + a(n-11) - a(n-12) for n>15.

%F Empirical g.f.: x*(370 - 400*x + 118*x^2 - 369*x^3 - 335*x^4 + 382*x^5 - 102*x^6 + 715*x^7 - 143*x^8 - 23*x^9 - 14*x^10 - 361*x^11 + 119*x^12 + 26*x^13 + 5*x^14) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2)*(1 - x - x^4)). - _Colin Barker_, Sep 01 2018

%e Some solutions for n=3:

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

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

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

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

%Y Cf. A224568.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013

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Last modified January 29 05:09 EST 2022. Contains 350672 sequences. (Running on oeis4.)