A155102 -id:A155102 - cp's OEIS frontend

A155103 Triangle read by rows: Matrix inverse of A155102.

1, 2, 1, 0, 0, 1, 6, 3, 0, 1, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 30, 15, 0, 5, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 28, 0, 0, 7, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0

Offset: 1

Mats Granvik, Jan 20 2009

A028361 appears in the first column at A036987 positions. A028362 appears in the second column, A155105 in the third and A155104 in the fourth. A000384 appears as the third ray from zero and A100147 as the fourth.

			Table begins:
1,
2,1,
0,0,1,
6,3,0,1,
0,0,0,0,1,
0,0,4,0,0,1,
0,0,0,0,0,0,1,
30,15,0,5,0,0,0,1,

Cf. A028361, A036987, A028362, A155105, A155104. A000384, A100147.

m = 14; t = Inverse[ Table[ Which[n == k, 1, n == 2*k, -k - 1, True, 0], {n, 1, m}, {k, 1, m}]]; Flatten[ Table[t[[n, k]], {n, 1, m}, {k, 1, n}]] (* Jean-François Alcover, Jul 19 2012 *)

A155105 Positive numbers appearing in the third column of A155103.

Original entry on oeis.org

1, 4, 28, 364, 9100, 445900, 43252300, 8347693900, 3213862151500, 2471459994503500, 3798634011551879500, 11673202317498925703500

Offset: 1

Mats Granvik, Jan 20 2009

Cf. A155103.

A155102 := proc(n,k) if n = k then 1 ; elif n =2*k then -k-1 ; else 0; end if; end proc:
A155103 := proc(amx) a := array(1..amx,1..amx) ; a[1,1] := 1/A155102(1,1) ;
        for r from 1 to amx do
                for c from 1 to r-1 do a[c,r] := 0 ; end do:
                a[r,r] := 1/A155102(r,r) ;
                for c from r-1 to 1 by -1 do a[r,c] := -add(a[cp,c]*A155102(r,cp),cp=c..r-1)/A155102(r,r) ;
                        if c = 3 and a[r,c] <> 0 then print( a[r,c]) ; end if;
                end do:
        end do:
        return ;
end proc:
A155103(290) ; # R. J. Mathar, Dec 07 2010

\\ after R. J. Mathar
T(n,k)=if(n==k,1,if(n==2*k,-(k+1))); \\ from A155102
\\ First term = 1 omitted
a155103(upto) = my(m=3*2^upto, a=matid(m)); for(r=1, m, forstep(c=r-1, 1, -1, a[r,c]=-sum(cp=c, r-1, a[cp,c]*T(r,cp)); if(c==3 && a[r,c]!=0, print1(a[r,c],", "))));
a155103(8) \\ Hugo Pfoertner, Oct 03 2024

From Tristan Cam, Oct 02 2024: (Start)
a(1) = 1, a(n) = a(n-1)*(1+3*2^(n-2)) (conjectured).
a(n) = Product_{k=1..n-1} 1+3*2^(k-1) = QPochhammer[-3, 2, n-1]. (conjectured). (End)

Two more terms from R. J. Mathar, Dec 07 2010

a(8)-a(12) from Hugo Pfoertner, Oct 02 2024

cp's OEIS Frontend

A155103 Triangle read by rows: Matrix inverse of A155102.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A155105 Positive numbers appearing in the third column of A155103.

Views

Author

Keywords

Crossrefs

Programs

Maple

PARI

Formula

Extensions