A154325 Triangle with interior all 2's and borders 1.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1

Offset

0,5

Comments

This triangle follows a general construction method as follows: Let a(n) be an integer sequence with a(0)=1, a(1)=1. Then T(n,k,r):=[k<=n](1+r*a(k)*a(n-k)) defines a symmetrical triangle.

Row sums are n + 1 + r*Sum_{k=0..n} a(k)*a(n-k) and central coefficients are 1+r*a(n)^2.

Here a(n)=1-0^n and r=1. Row sums are A004277.

Eigensequence of the triangle = A000129, the Pell sequence. - Gary W. Adamson, Feb 12 2009

Inverse has general element T(n,k)*(-1)^(n-k). - Paul Barry, Oct 06 2010

Links

Table of n, a(n) for n=0..65.

Formula

Number triangle T(n,k) = [k<=n](2-0^(n-k)-0^k+0^(n+k))=[k<=n](2-0^(k(n-k))).

a(n) = 2 - A103451(n). - Omar E. Pol, Jan 18 2009

Example

Triangle begins
  1;
  1, 1;
  1, 2, 1;
  1, 2, 2, 1;
  1, 2, 2, 2, 1;
  1, 2, 2, 2, 2, 1;
  1, 2, 2, 2, 2, 2, 1;
From Paul Barry, Oct 06 2010: (Start)
Production matrix is
  1,  1;
  0,  1, 1;
  0, -1, 0, 1;
  0,  1, 0, 0, 1;
  0, -1, 0, 0, 0, 1;
  0,  1, 0, 0, 0, 0, 1;
  0, -1, 0, 0, 0, 0, 0, 1;
  0,  1, 0, 0, 0, 0, 0, 0, 1; (End)

Crossrefs

Cf. A129765. - R. J. Mathar, Jan 14 2009

Cf. A103451. - Omar E. Pol, Jan 18 2009

Cf. A000129. - Gary W. Adamson, Feb 12 2009

Sequence in context: A134034 A174886 A157415 * A129765 A143187 A348042

Adjacent sequences: A154322 A154323 A154324 * A154326 A154327 A154328

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 07 2009

Status

approved