

A129638


Number of meaningful differential operations of the kth order on the space R^11.


6



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
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OFFSET

11,1


COMMENTS

Also number of meaningful compositions of the kth 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 zigzag paths from top to bottom of a rectangle of width 12, whose color is that of the top right corner. [Joseph Myers, Dec 23 2008]


LINKS

Table of n, a(n) for n=11..40.
B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 2933.
B. Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux Directional Derivative , arXiv:0706.0249 [math.CO], 2007.
Joseph Myers, BMO 20082009 Round 1 Problem 1Generalisation
Index entries for linear recurrences with constant coefficients, signature (1,5,4,6,3,1).


FORMULA

a(k+6) = a(k+5) +5*a(k+4) 4*a(k+3) 6*a(k+2) +3*a(k+1) +a(k).
G.f.: x^11*(6*x^5+21*x^424*x^336*x^2+10*x+11)/(x^6+3*x^56*x^44*x^3+5*x^2+x1). [Colin Barker, Jul 08 2012]


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))^(k1), k=1, matrix(n, n, Identity)); return(evalm(v&*A&*transpose(v))[1, 1]); end:


MATHEMATICA

LinearRecurrence[{1, 5, 4, 6, 3, 1}, {11, 21, 40, 77, 148, 286}, 30] (* JeanFrançois Alcover, Oct 10 2017 *)


CROSSREFS

Cf. A090989A090995.
Cf. A000079, A007283, A020701, A020714.
Sequence in context: A146246 A215968 A064832 * A127624 A097616 A146150
Adjacent sequences: A129635 A129636 A129637 * A129639 A129640 A129641


KEYWORD

nonn,easy


AUTHOR

Branko Malesevic, May 31 2007


EXTENSIONS

More terms from Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 20 2007
More terms from Joseph Myers, Dec 23 2008


STATUS

approved



