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A034007
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First differences of A045891.
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15
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1, 0, 2, 4, 9, 20, 44, 96, 208, 448, 960, 2048, 4352, 9216, 19456, 40960, 86016, 180224, 376832, 786432, 1638400, 3407872, 7077888, 14680064, 30408704, 62914560, 130023424, 268435456, 553648128, 1140850688, 2348810240
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let M_n be the n X n matrix m_(i,j)=4+abs(i-j) then det(M_n)=(-1)^(n+1)*a(n+2) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 28 2002
Number of ordered pairs of (possibly empty) ordered partitions, each not beginning with 1. - Christian G. Bower (bowerc(AT)usa.net), Jan 23 2004
If X_1,X_2,...,X_n are 2-blocks of a (2n+4)-set X then, for n>=1, a(n+3) is the number of (n+1)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
F. Ellermann, Illustration of binomial transforms
Milan Janjic, Two Enumerative Functions
Index to sequences with linear recurrences with constant coefficients, signature (4,-4).
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FORMULA
| Sum_{ k = 0..n } (k+4)*binomial(n,k) gives 4, 9, 20, 44, 96, 208, 448, 960, 2048, 4352, ... - N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2008
a(n) = (n+5)*2^(n-4), n >= 3; a(0)=1, a(1)=0, a(2)=2. G.f.: ((1-x)^2/(1-2*x))^2.
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MATHEMATICA
| Join[{1, 0, 2, a=4}, Table[a=(2*(n+7)*a)/(n+6), {n, 2, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 15 2011*)
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PROG
| (PARI) a(n)=if(n<3, [1, 0, 2][n+1], (n+5)*2^(n-4)) \\ Charles R Greathouse IV, Jun 01 2011
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CROSSREFS
| Cf. A045891. Convolution of A034008 with itself.
Columns of A091613 converge to this sequence.
Sequence in context: A123720 A179744 * A109975 A129891 A130587 A129988
Adjacent sequences: A034004 A034005 A034006 * A034008 A034009 A034010
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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