11,1

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]

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).

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]

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:

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

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

nonn,easy

Branko Malesevic, May 31 2007

More terms from Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 20 2007

More terms from Joseph Myers, Dec 23 2008

approved