A131035 Triangle read by rows: A051340 * A129686 as infinite lower triangular matrices.

1, 2, 1, 4, 1, 1, 5, 2, 1, 1, 6, 2, 2, 1, 1, 7, 2, 2, 2, 1, 1, 8, 2, 2, 2, 2, 1, 1, 9, 2, 2, 2, 2, 2, 1, 1, 10, 2, 2, 2, 2, 2, 2, 1, 1, 11, 2, 2, 2, 2, 2, 2, 2, 1, 1, 12, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 14, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

G.f.: (1 + (1 - y)*x^2 - x^3)/((1 - x)^2*(1 - x*y)). - Andrew Howroyd, Sep 22 2025

Example

First few rows of the triangle:
   1;
   2, 1;
   4, 1, 1;
   5, 2, 1, 1;
   6, 2, 2, 1, 1;
   7, 2, 2, 2, 1, 1;
   8, 2, 2, 2, 2, 1, 1;
   9, 2, 2, 2, 2, 2, 1, 1;
  10, 2, 2, 2, 2, 2, 2, 1, 1;
  ...

Prog

(PARI) M(n)={matrix(n, n, i, j, if(j==1, i, j<=i)) * matrix(n, n, i, j, if(j<=i, abs(i-j-1)==1))}
{ my(A=M(10)); for(i=1, #A, print(A[i, 1..i])) } \\ Andrew Howroyd, Sep 22 2025
(PARI) T(n) = [Vecrev(p) | p<-Vec((1 + (1 - y)*x^2 - x^3)/((1 - x)^2*(1 - x*y)) + O(x^n))]
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Sep 22 2025

Crossrefs

Row sums are A008486(n).

Cf. A051340, A129686, A131034.

Sequence in context: A162944 A140582 A062866 * A339833 A118745 A235671

Adjacent sequences: A131032 A131033 A131034 * A131036 A131037 A131038

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 10 2007

Extensions

Offset changed and a(46) onwards from Andrew Howroyd, Sep 22 2025

Status

approved