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A090994
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Number of meaningful differential operations of the n-th order on the space R^9.
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4
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9, 17, 32, 61, 116, 222, 424, 813, 1556, 2986, 5721, 10982, 21053, 40416, 77505, 148785, 285380, 547810, 1050876, 2017126, 3869845, 7427671, 14250855, 27351502, 52479500, 100719775, 193258375, 370895324, 711682501, 1365808847, 2620797529
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Also number of meaningful compositions of the n-th order of the differential operations and Gateaux directional derivative on the space R^8. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007
Also (starting 5,9,...) the number of zig-zag paths from top to bottom of a rectangle of width 10, whose color is that of the top right corner. [From Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008]
Also, number of n-digit terms in A033075 (stated without proof in A033075). - Zak Seidov, Feb 02 2011
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LINKS
| 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.
B. Malesevic and I. Jovovic, TheCompositions of the Differential Operations and Gateaux Directional Derivative , arxiv:0706.0249
Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
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FORMULA
| a(k+5)=a(k+4)+4*a(k+3)-3*a(k+2)-3*a(k+1)+a(k)
G.f.: x*(9+8*x-21*x^2-12*x^3+5*x^4)/ (1-x-4*x^2+3*x^3+3*x^4-x^5) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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MAPLE
| NUM := proc(k :: integer) local i, j, n, Fun, Identity, v, A; n := 9; # <- 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, A000079, A007283, A020701, A020714, A129638, A033075.
Sequence in context: A147459 A188559 A014004 * A164887 A111733 A127193
Adjacent sequences: A090991 A090992 A090993 * A090995 A090996 A090997
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KEYWORD
| nonn
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AUTHOR
| Branko Malesevic (malesevic(AT)kiklop.etf.bg.ac.yu), Feb 29 2004
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
More terms from Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008
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