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A154325 Triangle with interior all 2's and borders 1. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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. [From Gary W. Adamson, Feb 12 2009]

Inverse has general element T(n,k)*(-1)^(n-k). [From 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). [From 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

Contribution 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. [From R. J. Mathar, Jan 14 2009]

Cf. A103451. [From Omar E. Pol, Jan 18 2009]

A000129 [From Gary W. Adamson, Feb 12 2009]

Sequence in context: A134034 A174886 A157415 * A129765 A143187 A143209

Adjacent sequences:  A154322 A154323 A154324 * A154326 A154327 A154328

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 07 2009

STATUS

approved

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Last modified February 26 10:24 EST 2020. Contains 332278 sequences. (Running on oeis4.)