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Search: id:A090990
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| A090990 |
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Number of meaningful differential operations of the n-th order on the space R^5. |
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+0
5
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| 5, 9, 16, 29, 52, 94, 169, 305, 549, 990, 1783, 3214, 5790, 10435, 18801, 33881, 61048, 110009, 198224, 357194, 643633, 1159797, 2089869, 3765830, 6785771, 12227562, 22033274, 39702627, 71541613, 128913593, 232294192, 418579765
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also number of meaningful compositions of the n-th order of the differential operations and Gateaux directional derivative on the space R^4. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007
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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
B. Malesevic and I. Jovovic, TheCompositions of the Differential Operations and Gateaux DirectionalDerivative .
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FORMULA
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a(k+3)=a(k+2)+2*a(k+1)-a(k)
G.f.: x(5+4x-3x^2)/(1-x-2x^2+x^3). - Ralf Stephan, Aug 19 2004
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MAPLE
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NUM := proc(k :: integer) local i, j, n, Fun, Identity, v, A; n := 5; # <- 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.
Cf. A000079, A007283, A020701, A020714, A129638.
Sequence in context: A020958 A020750 A020713 this_sequence A088495 A062777 A102179
Adjacent sequences: A090987 A090988 A090989 this_sequence A090991 A090992 A090993
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KEYWORD
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nonn
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AUTHOR
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Branko Malesevic (malesevic(AT)kiklop.etf.bg.ac.yu), Feb 29 2004
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EXTENSIONS
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More terms from Ralf Stephan, Aug 19 2004
More terms from Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007
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