0,5

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. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 12 2009]

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). [From Omar E. Pol (info(AT)polprimos.com), Jan 18 2009]

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

Cf. A129765. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 14 2009]

Cf. A103451. [From Omar E. Pol (info(AT)polprimos.com), Jan 18 2009]

A000129 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 12 2009]

Sequence in context: A023589 A134034 A157415 this_sequence A129765 A143187 A143209

Adjacent sequences: A154322 A154323 A154324 this_sequence A154326 A154327 A154328

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), Jan 07 2009