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

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, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Omar E. Pol, Nov 30 2010, Dec 01 2010

Keywords

• nonn
• tabl
• more

Comments

The same idea as A182742 but for odd integers.

Examples

			Array begins:
3,2,2,2,2,2,2,2,2,2,2,
5,2,2,2,2,2,2,2,2,2,
4,3,2,2,2,2,2,2,2,2,
7,2,2,2,2,2,2,2,2,
3,3,3,2,2,2,2,2,2,2,
6,3,2,2,2,2,2,2,2,
5,4,2,2,2,2,2,2,2,
9,2,2,2,2,2,2,2,
5,3,3,2,2,2,2,2,2,
4,4,3,2,2,2,2,2,2,
8,3,2,2,2,2,2,2,
7,4,2,2,2,2,2,2,
6,5,2,2,2,2,2,2,
11,2,2,2,2,2,2,
4,3,3,3,2,2,2,2,2,
7,3,3,2,2,2,2,2,
6,4,3,2,2,2,2,2,
5,5,3,2,2,2,2,2,
10,3,2,2,2,2,2,
5,4,4,2,2,2,2,2,
9,4,2,2,2,2,2,
8,5,2,2,2,2,2,
7,6,2,2,2,2,2,
		

Links

• Omar E. Pol, Illustration of the shell model of partitions (3D view)

Crossrefs

Cf. A135010, A138121, A141285, A182731, A182742.

Column 1 give A182733. Column 2 give A182745.

Programs

Maple

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:
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:
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:
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