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%I #13 Jun 05 2021 06:48:24
%S 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,
%T 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
%N Triangle with interior all 2's and borders 1.
%C 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.
%C Row sums are n + 1 + r*Sum_{k=0..n} a(k)*a(n-k) and central coefficients are 1+r*a(n)^2.
%C Here a(n)=1-0^n and r=1. Row sums are A004277.
%C Eigensequence of the triangle = A000129, the Pell sequence. - _Gary W. Adamson_, Feb 12 2009
%C Inverse has general element T(n,k)*(-1)^(n-k). - _Paul Barry_, Oct 06 2010
%F Number triangle T(n,k) = [k<=n](2-0^(n-k)-0^k+0^(n+k))=[k<=n](2-0^(k(n-k))).
%F a(n) = 2 - A103451(n). - _Omar E. Pol_, Jan 18 2009
%e Triangle begins
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 2, 2, 1;
%e 1, 2, 2, 2, 1;
%e 1, 2, 2, 2, 2, 1;
%e 1, 2, 2, 2, 2, 2, 1;
%e From _Paul Barry_, Oct 06 2010: (Start)
%e Production matrix is
%e 1, 1;
%e 0, 1, 1;
%e 0, -1, 0, 1;
%e 0, 1, 0, 0, 1;
%e 0, -1, 0, 0, 0, 1;
%e 0, 1, 0, 0, 0, 0, 1;
%e 0, -1, 0, 0, 0, 0, 0, 1;
%e 0, 1, 0, 0, 0, 0, 0, 0, 1; (End)
%Y Cf. A129765. - _R. J. Mathar_, Jan 14 2009
%Y Cf. A103451. - _Omar E. Pol_, Jan 18 2009
%Y Cf. A000129. - _Gary W. Adamson_, Feb 12 2009
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Jan 07 2009
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