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 A100314 Number of 2 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1). 9
 1, 4, 8, 14, 24, 42, 76, 142, 272, 530, 1044, 2070, 4120, 8218, 16412, 32798, 65568, 131106, 262180, 524326, 1048616, 2097194, 4194348, 8388654, 16777264, 33554482, 67108916, 134217782, 268435512, 536870970, 1073741884, 2147483710, 4294967360, 8589934658 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1 0, a(n) = 2*A005126(n-1). (End) G.f.: 1 + 2x(2-4x+x^2)/((1-x)^2*(1-2x)). a(n+1)-a(n) = A052548(n). - R. J. Mathar, Jun 13 2008 From Colin Barker, Oct 16 2013: (Start) a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). G.f.: (3*x^2 - 1) / ((x - 1)^2*(2*x - 1)). (End) E.g.f.: exp(2*x) + 2*x*exp(x). - Franck Maminirina Ramaharo, Dec 19 2018 a(n) = A000079(n) + A005843(n). - Muniru A Asiru, Dec 21 2018 MAPLE a:= proc(n) 2^n + 2*n: end: seq(a(n), n=0..50); # Gary W. Adamson, Jul 20 2007 PROG (MAGMA) [2^n+2*n: n in [1..40]]; // Vincenzo Librandi, Oct 22 2011 (Maxima) makelist(2^n + 2*n, n, 0, 50); /* Franck Maminirina Ramaharo, Dec 19 2018 */ (GAP) List([0..40], n->2^n+2*n); # Muniru A Asiru, Dec 21 2018 CROSSREFS Cf. m=3: A100315; m=4: A100316. Row sums of A131830. Cf. A005126, A052548, A099003. Cf. A000051, A000079, A001787, A002064, A005126, A058331, A100314, A131830, A132750, A176691. Sequence in context: A060064 A045474 A131831 * A105143 A020185 A008029 Adjacent sequences:  A100311 A100312 A100313 * A100315 A100316 A100317 KEYWORD nonn,easy AUTHOR Sergey Kitaev, Nov 13 2004 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Dec 21 2018 STATUS approved

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Last modified October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)