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A013979
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Expansion of 1/(1-x^2-x^3-x^4) = 1/( (1+x)*(1-x-x^3) ).
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7
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1, 0, 1, 1, 2, 2, 4, 5, 8, 11, 17, 24, 36, 52, 77, 112, 165, 241, 354, 518, 760, 1113, 1632, 2391, 3505, 5136, 7528, 11032, 16169, 23696, 34729, 50897, 74594, 109322, 160220, 234813, 344136, 504355, 739169, 1083304, 1587660, 2326828, 3410133, 4997792
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OFFSET
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0,5
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COMMENTS
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For n>0, number of ordered partitions of n into 2's, 3's and 4's. - Len Smiley (smiley(AT)math.uaa.alaska.edu), May 08 2001
Diagonal sums of trinomial triangle A071675 (Riordan array (1, x(1+x+x^2))). - Paul Barry, Feb 15 2005
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REFERENCES
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C. K. Fan, A Hecke algebra quotient and some combinatorial applications. J. Algebraic Combin. 5 (1996), no. 3, 175-189.
C. K. Fan, Structure of a Hecke algebra quotient. J. Amer. Math. Soc. 10 (1997), no. 1, 139-167. [Page 156, f^0_n.]
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (0,1,1,1).
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FORMULA
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a(n)=sum{k=0..floor(n/2), sum{i=0..floor(n/2), C(k, 2i+3k-n)C(2i+3k-n, i)}}; - Paul Barry, Feb 15 2005
a(n) = a(n-4) + a(n-3) + a(n-2). - Jon Schoenfield (jonscho(AT)hiwaay.net), Aug 07 2006
a(n)+a(n+1) = A000930(n+1). - R. J. Mathar, Mar 14 2011
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MATHEMATICA
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a=b=c=0; d=1; lst={d}; Do[AppendTo[lst, e=a+b+c]; a=b; b=c; c=d; d=e, {n, 0, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, May 28 2010]
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PROG
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(Haskell)
a013979 n = a013979_list !! n
a013979_list = 1 : 0 : 1 : 1 : zipWith (+) a013979_list
(zipWith (+) (tail a013979_list) (drop 2 a013979_list))
-- Reinhard Zumkeller, Mar 23 2012
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CROSSREFS
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Cf. A060945 (Ordered partitions into 1's, 2's and 4's), A107458.
First differences of A023435.
Cf. A001634.
Sequence in context: A109434 A089299 A017910 * A107458 A060280 A006206
Adjacent sequences: A013976 A013977 A013978 * A013980 A013981 A013982
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Vladimir Joseph Stephan Orlovsky, May 28 2010
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STATUS
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approved
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