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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. - 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

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)