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A079859
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a(n) = n*2^(n-4)
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7
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4, 10, 24, 56, 128, 288, 640, 1408, 3072, 6656, 14336, 30720, 65536, 139264, 294912, 622592, 1310720, 2752512, 5767168, 12058624, 25165824, 52428800, 109051904, 226492416, 469762048, 973078528, 2013265920, 4160749568, 8589934592
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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COMMENTS
| a(n) = the number of occurrences of 3s in the palindromic compositions of m = 2*n-1 = the number of occurrences of 4s in the palindromic compositions of k = 2*n.
This sequence is part of a family of sequences, namely R(n,k), the number of ks in palindromic compositions of n. See also A057711, A001792, A078836, A079861, A079862, A079863. General formula: R(n,k)=2^(floor(n/2) - k) * (2 + floor(n/2) - k) if n and k have different parity and R(n,k)=2^(floor(n/2) - k) * (2 + floor(n/2) - k + 2^(floor((k+1)/2 - 1)) otherwise, for n >= 2k.
Number of 2 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (01;1). 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<i2, j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 4..1000
P. Chinn, R. Grimaldi and S. Heubach, The frequency of summands of a particular size ..., Ars Combin. 69 (2003), 65-78.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
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FORMULA
| O.g.f.: 2x^4(2-3x)/(1-2x)^2. a(n)=2*A045623(n-3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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EXAMPLE
| a(4)=4 since the palindromic compositions of 7 that contain a 3 are 2+3+2, 1+1+3+1+1 and 3+1+3, for a total of 4 3s. The palindromic compositions of 8 that contain a 4 are 2+4+2, 1+1+4+1+1 and 4+4.
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MATHEMATICA
| Table[i*2^(i - 4), {i, 4, 50}]
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PROG
| (MAGMA) [n*2^(n-4) : n in [4..40]]; // Vincenzo Librandi, Sep 22 2011
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CROSSREFS
| Cf. A057711, A001792, A078836, A079861, A079862.
Main diagonal of A049089.
Sequence in context: A052252 A087447 A129953 * A118871 A019494 A192886
Adjacent sequences: A079856 A079857 A079858 * A079860 A079861 A079862
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KEYWORD
| easy,nonn
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AUTHOR
| Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003
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