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Search: id:A129639
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| A129639 |
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Number of meaningful differential operations of the k-th order on the space R^12. |
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+0
3
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| 12, 22, 40, 74, 136, 252, 464, 860, 1584, 2936, 5408, 10024, 18464, 34224, 63040, 116848, 215232, 398944, 734848, 1362080, 2508928, 4650432, 8566016, 15877568, 29246208, 54209408, 99852800, 185082496, 340918784, 631911168, 1163969536
(list; graph; listen)
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OFFSET
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12,1
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COMMENT
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Also (starting 7,12,...) the number of zig-zag paths from top to bottom of a rectangle of width 7. [From Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008]
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REFERENCES
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B. Malesevic: Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.
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LINKS
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B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n
Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
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FORMULA
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f(k+6)=6*f(k+4)-10*f(k+2)+4*f(k)
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MAPLE
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NUM := proc(k :: integer) local i, j, n, Fun, Identity, v, A; n:=12; # <- DIMENSION Fun:=(i, j)->piecewise(((j=i+1) or (i+j=n+1)), 1, 0); Identity:=(i, j)->piecewise(i=j, 1, 0); v:=matrix(1, n, 1); A:=piecewise(k>1, (matrix(n, n, Fun))^(k-1), k=1, matrix(n, n, Identity)); return(evalm(v&*A&*transpose(v))[1, 1]); end:
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CROSSREFS
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Cf. A090989-A090995.
Sequence in context: A098955 A124885 A115745 this_sequence A153361 A115709 A115703
Adjacent sequences: A129636 A129637 A129638 this_sequence A129640 A129641 A129642
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KEYWORD
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nonn
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AUTHOR
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Branko Malesevic (malesevic(AT)etf.bg.ac.yu), May 31 2007
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EXTENSIONS
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More terms from Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008
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