1,1

Also number of meaningful compositions of the n-th order of the differential operations and Gateaux directional derivative on the space R^8. - Branko Malesevic and Ivana Jovovic (ivana121(AT)EUnet.yu), Jun 21 2007

Also (starting 5,9,...) the number of zig-zag paths from top to bottom of a rectangle of width 10, 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, TheCompositions of the Differential Operations and Gateaux DirectionalDerivative .

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

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

G.f.: x*(9+8*x-21*x^2-12*x^3+5*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

NUM := proc(k :: integer) local i, j, n, Fun, Identity, v, A; n := 9; # <- 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, A129638.

Sequence in context: A081030 A147459 A014004 this_sequence A164887 A111733 A127193

Adjacent sequences: A090991 A090992 A090993 this_sequence A090995 A090996 A090997

nonn

Branko Malesevic (malesevic(AT)kiklop.etf.bg.ac.yu), Feb 29 2004

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

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