A129638 Number of meaningful differential operations of the k-th order on the space R^11.

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

Offset

11,1

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. [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), 29-33.

B. Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux Directional Derivative , arXiv:0706.0249 [math.CO], 2007.

Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation

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^4-24*x^3-36*x^2+10*x+11)/(x^6+3*x^5-6*x^4-4*x^3+5*x^2+x-1). [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))^(k-1), 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] (* Jean-François Alcover, Oct 10 2017 *)

Crossrefs

Cf. A090989-A090995.

Cf. A000079, A007283, A020701, A020714.

Sequence in context: A146246 A215968 A064832 * A333356 A127624 A097616

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