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 A224670 Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent 1
 25, 50, 76, 123, 191, 300, 470, 741, 1173, 1866, 2980, 4775, 7671, 12348, 19906, 32125, 51885, 83846, 135548, 219191, 354515, 573460, 927706, 1500873, 2428261, 3928790, 6356680, 10285071, 16641323, 26925936, 43566770, 70492185, 114058401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 2 of A224676. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5). Conjectures from Colin Barker, Feb 17 2018: (Start) G.f.: x*(25 - 50*x + x^2 + 44*x^3 - 21*x^4) / ((1 - x)^3*(1 - x - x^2)). a(n) = -2 + 2^(1-n)*sqrt(5)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) + 2*(1+n) + (1+n)*(2+n)/2. (End) EXAMPLE Some solutions for n=3: ..1..0..2....0..0..0....1..1..1....1..0..0....1..0..0....0..0..0....1..0..0 ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..0....0..0..0 ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..0..0 ..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....1..1..1....0..0..0 CROSSREFS Sequence in context: A031472 A045210 A169860 * A045195 A232438 A034025 Adjacent sequences:  A224667 A224668 A224669 * A224671 A224672 A224673 KEYWORD nonn AUTHOR R. H. Hardin, Apr 14 2013 STATUS approved

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Last modified July 26 20:56 EDT 2021. Contains 346300 sequences. (Running on oeis4.)