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A182743 Table of the partitions that do not contain 1 as a part for odd integers.

%I A182743 #12 May 29 2016 09:54:55
%S A182743 3,5,2,4,2,2,7,3,2,2,3,2,2,2,2,6,3,2,2,2,2,5,3,3,2,2,2,2,9,4,2,2,2,2,
%T A182743 2,2,5,2,2,2,2,2,2,2,2,4,3,2,2,2,2,2,2,2,2
%N A182743 Table of the partitions that do not contain 1 as a part for odd integers.
%C A182743 The same idea as A182742 but for odd integers.
%H A182743 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa3dt.jpg">Illustration of the shell model of partitions (3D view)</a>
%e A182743 Array begins:
%e A182743 3,2,2,2,2,2,2,2,2,2,2,
%e A182743 5,2,2,2,2,2,2,2,2,2,
%e A182743 4,3,2,2,2,2,2,2,2,2,
%e A182743 7,2,2,2,2,2,2,2,2,
%e A182743 3,3,3,2,2,2,2,2,2,2,
%e A182743 6,3,2,2,2,2,2,2,2,
%e A182743 5,4,2,2,2,2,2,2,2,
%e A182743 9,2,2,2,2,2,2,2,
%e A182743 5,3,3,2,2,2,2,2,2,
%e A182743 4,4,3,2,2,2,2,2,2,
%e A182743 8,3,2,2,2,2,2,2,
%e A182743 7,4,2,2,2,2,2,2,
%e A182743 6,5,2,2,2,2,2,2,
%e A182743 11,2,2,2,2,2,2,
%e A182743 4,3,3,3,2,2,2,2,2,
%e A182743 7,3,3,2,2,2,2,2,
%e A182743 6,4,3,2,2,2,2,2,
%e A182743 5,5,3,2,2,2,2,2,
%e A182743 10,3,2,2,2,2,2,
%e A182743 5,4,4,2,2,2,2,2,
%e A182743 9,4,2,2,2,2,2,
%e A182743 8,5,2,2,2,2,2,
%e A182743 7,6,2,2,2,2,2,
%p A182743 cmpL := proc(a,b) local i ; for i from 1 to min(nops(a),nops(b)) do if op(i,a) < op(i,b) then return -1 ; elif op(i,a) > op(i,b) then return 1 ; end if; end do; if nops(a) > nops(b) then return 1; elif nops(a) < nops(b) then return -1; else return 0; end if; end proc:
%p A182743 pShellMin := proc(p) local idx,j; idx := 1 ; for j from 2 to nops(p) do if cmpL( op(j,p),op(idx,p)) < 0 then idx := j; end if; end do; return idx ; end proc:
%p A182743 A141285rowf := proc(n) local p; if n <= 1 then [n] ; else psort := [] ; p := combinat[partition](n) ; while nops(p) > 0 do m := pShellMin(p) ; mmi := min(op(op(m,p))) ; if mmi > 1 then mma := max(op(op(m,p))) ; psort := [op(psort),sort(op(m,p),`>`)] ; end if; p := subsop(m=NULL,p) ; end do: psort ; end if; end proc:
%p A182743 for n from 1 to 17 by 2 do shl := A141285rowf(n) ; for r in shl do for k in r do printf("%d,",k) ; end do: printf("\n") ; end do: printf("\n") ; end do: # _R. J. Mathar_, Dec 03 2010
%Y A182743 Cf. A135010, A138121, A141285, A182731, A182742.
%Y A182743 Column 1 give A182733. Column 2 give A182745.
%K A182743 nonn,tabl,more
%O A182743 1,1
%A A182743 _Omar E. Pol_, Nov 30 2010, Dec 01 2010