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 A208638 Number of 3 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors. 2
 4, 13, 32, 71, 150, 309, 628, 1267, 2546, 5105, 10224, 20463, 40942, 81901, 163820, 327659, 655338, 1310697, 2621416, 5242855, 10485734, 20971493, 41943012, 83886051, 167772130, 335544289, 671088608, 1342177247, 2684354526, 5368709085 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 3 of A208637. Possibly row 4 of the convolution array A213568. - Clark Kimberling, Jun 20 2012 From Noah Carey, Aug 31 2021: (Start) Conjecture: a(n) is equal to half the sum along the edges of (centered, height 2, width n, starting at line n+1) rectangles in Pascal's triangle, as shown here for n=3 (not including the terms inside the rectangles):                 1               1   1             1   2   1     a(3) = (4+6+4 + 15+20+15)/2           1   3   3   1         1   4---6---4   1       1   5 |       | 5   1     1   6  15--20--15   6   1   1   7  21  35  35  20   7   1 (End) 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) + 2*a(n-3). Conjectures from Colin Barker, Mar 07 2018: (Start) G.f.: x*(4 - 3*x) / ((1 - x)^2*(1 - 2*x)). a(n) = 5*2^n - n - 5. (End) EXAMPLE Some solutions for n=4:   0 1 0 1     0 0 1 0     0 1 0 0     0 0 0 1     0 0 0 0   0 1 0 0     1 0 1 0     0 1 1 1     1 1 0 0     1 1 1 0   1 0 1 0     1 0 1 0     1 0 0 1     0 1 1 1     0 0 1 1 CROSSREFS Cf. A208637. Sequence in context: A037235 A051912 A060099 * A173277 A036420 A266094 Adjacent sequences:  A208635 A208636 A208637 * A208639 A208640 A208641 KEYWORD nonn AUTHOR R. H. Hardin, Feb 29 2012 STATUS approved

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Last modified July 4 01:37 EDT 2022. Contains 355063 sequences. (Running on oeis4.)