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. [From Joseph Myers (jsm(AT)polyomino.org.uk), 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, Some combinatorial aspects of differential operation composition on the space R^n

B. Malesevic and I. Jovovic, The Compositions of the Differential Operations and Gateaux Directional Derivative .

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

f(k+6)=f(k+5)+5*f(k+4)-4*f(k+3)-6*f(k+2)+3*f(k+1)+f(k)

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:

Cf. A090989-A090995.

Cf. A000079, A007283, A020701, A020714.

Sequence in context: A145060 A146246 A064832 this_sequence A127624 A097616 A146150

Adjacent sequences: A129635 A129636 A129637 this_sequence A129639 A129640 A129641

nonn

Branko Malesevic (malesevic(AT)etf.bg.ac.yu), May 31 2007

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

More terms from Joseph Myers (jsm(AT)polyomino.org.uk), Dec 23 2008