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A129638
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Number of meaningful differential operations of the k-th order on the space R^11.
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6
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11, 21, 40, 77, 148, 286, 552, 1069, 2068, 4010, 7768, 15074, 29225, 56736, 110055, 213705, 414676, 805314, 1562977, 3035514, 5892257, 11443768, 22215753, 43146726, 83766396, 162686691, 315860810, 613439352, 1191054193, 2313133481
(list; graph; refs; listen; history; internal format)
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OFFSET
| 11,1
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COMMENTS
| Also number of meaningful compositions of the k-th order of the differential operations and Gateaux directional derivative on the space R^10. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 20 2007
Also (starting 6,11,...) the number of zig-zag paths from top to bottom of a rectangle of width 12, whose color is that of the top right corner. [From Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008]
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REFERENCES
| 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
| B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n
B. Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux Directional Derivative .
Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
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FORMULA
| f(k+6)=f(k+5)+5*f(k+4)-4*f(k+3)-6*f(k+2)+3*f(k+1)+f(k)
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MAPLE
| NUM := proc(k :: integer) local i, j, n, Fun, Identity, v, A; n:=11; # <- 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
| Cf. A090989-A090995.
Cf. A000079, A007283, A020701, A020714.
Sequence in context: A145060 A146246 A064832 * A127624 A097616 A146150
Adjacent sequences: A129635 A129636 A129637 * A129639 A129640 A129641
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KEYWORD
| nonn
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AUTHOR
| Branko Malesevic (malesevic(AT)etf.bg.ac.yu), May 31 2007
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EXTENSIONS
| More terms from Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 20 2007
More terms from Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008
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