1,4

G.f.: Product(1+x^n/(1-y*x^n),n=1..inf).

1

1,1

2,0,1

2,2,0,1

3,2,1,0,1

4,2,3,1,0,1

5,4,2,2,1,0,1

6,6,3,3,2,1,0,1

8,7,5,4,2,2,1,0,1

10,8,10,3,5,2,2,1,0,1

12,13,8,9,4,4,2,2,1,0,1

15,15,14,10,8,5,4,2,2,1,0,1

18,21,15,16,8,9,4,4,2,2,1,0,1

(PARI) partitm(n, m, nmin)={ local(resul, partj) ; if( n < 0 || m <0, return([; ]) ; ) ; resul=matrix(0, m); if(m==0, return(resul); ) ; for(j=max(1, nmin), n\m, partj=partitm(n-j, m-1, j) ; for(r1=1, matsize(partj)[1], resul=concat(resul, concat([j], partj[r1, ])) ; ) ; ) ; if(m==1 && n >= nmin, resul=concat(resul, [[n]]) ; ) ; return(resul) ; } partit(n)={ local(resul, partm, filr) ; if( n < 0, return([; ]) ; ) ; resul=matrix(0, n) ; for(m=1, n, partm=partitm(n, m, 1) ; filr=vector(n-m) ; for(r1=1, matsize(partm)[1], resul=concat( resul, concat(partm[r1, ], filr) ) ; ) ; ) ; return(resul) ; } A133121row(n)={ local(p=partit(n), resul=vector(n), nprts, ndprts) ; for(r=1, matsize(p)[1], nprts=0 ; ndprts=0 ; for(c=1, n, if( p[r, c]==0, break, nprts++ ; if(c==1, ndprts++, if(p[r, c]!=p[r, c-1], ndprts++ ) ; ) ; ) ; ) ; k=nprts-ndprts; resul[k+1]++ ; ) ; return(resul) ; } A133121()={ for(n=1, 20, arow=A133121row(n) ; for(k=1, n, print1(arow[k], ", ") ; ) ; ) ; } A133121() ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 28 2007

Cf. A000009, A090858.

Adjacent sequences: A133118 A133119 A133120 this_sequence A133122 A133123 A133124

Sequence in context: A062169 A113680 A128187 this_sequence A091602 A035465 A096144

easy,nonn,tabl

Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 18 2007

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 28 2007