A131034 Triangle read by rows: A129686 * A051340 as infinite lower triangular matrices.

1, 2, 1, 4, 1, 1, 6, 2, 1, 1, 8, 2, 2, 1, 1, 10, 2, 2, 2, 1, 1, 12, 2, 2, 2, 2, 1, 1, 14, 2, 2, 2, 2, 2, 1, 1, 16, 2, 2, 2, 2, 2, 2, 1, 1, 18, 2, 2, 2, 2, 2, 2, 2, 1, 1, 20, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 22, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 24, 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

Equals A129686 * A051340 as infinite lower triangular matrices.

G.f.: (1 + (1 - y)*x^2 - y*x^4)/((1 - x)^2*(1 - y*x)). - Andrew Howroyd, Sep 22 2025

Example

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

Prog

(PARI) M(n)={matrix(n, n, i, j, if(j<=i, abs(i-j-1)==1)) * matrix(n, n, i, j, if(j==1, i, j<=i))}
{ 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 - y*x^4)/((1 - x)^2*(1 - y*x)) + O(x^n))]
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Sep 22 2025

Crossrefs

Row sums are A113127.

Cf. A129686, A051340, A131035.

Sequence in context: A118745 A235671 A375495 * A346873 A130313 A247073

Adjacent sequences: A131031 A131032 A131033 * A131035 A131036 A131037

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 10 2007

Extensions

Missing a(20) inserted and a(45) onwards from Andrew Howroyd, Sep 22 2025

Status

approved