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A167769 Pendular trinomial triangle (p=0), read by rows of 2n+1 terms (n>=0), defined by the recurrence : if 0<k<n T(n,k)= T(n-1,k)+p*T(n,2n-1-k); else if n-1<k<2n-1, T(n,k)= T(n-1,k)+T(n,2n-2-k); with T(n,0)=T(n+1,2n)=1 and T(n+1,2n+1)=T(n+1,2n+2)=0. 1

%I

%S 1,1,0,0,1,1,1,0,0,1,2,3,2,1,0,0,1,3,6,8,6,3,1,0,0,1,4,10,18,24,18,10,

%T 4,1,0,0,1,5,15,33,57,75,57,33,15,5,1,0,0,1,6,21,54,111,186,243,186,

%U 111,54,21,6,1,0,0,1,7,28,82,193,379,622,808,622,379,193,82,28,7,1,0,0

%N Pendular trinomial triangle (p=0), read by rows of 2n+1 terms (n>=0), defined by the recurrence : if 0<k<n T(n,k)= T(n-1,k)+p*T(n,2n-1-k); else if n-1<k<2n-1, T(n,k)= T(n-1,k)+T(n,2n-2-k); with T(n,0)=T(n+1,2n)=1 and T(n+1,2n+1)=T(n+1,2n+2)=0.

%C See A119369 for p=1 and A122445 for p=2. The diagonals may be generated by iterated convolutions of a base sequence B (A000108(n)) with the sequence C (A000957(n+1)) of central terms.

%D Kim, Ki Hang; Rogers, Douglas G.; Roush, Fred W. Similarity relations and semiorders. Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 577--594, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979. MR0561081 (81i:05013) - From _N. J. A. Sloane_, Jun 05 2012

%e Triangle begins : 1 ; 1,0,0 ; 1,1,1,0,0 ; 1,2,3,2,1,0,0 ; 1,3,6,8,6,3,1,0,0 ; ...

%o (PARI) T(n, k)=if(k==0 && n==0, 1, if(k>2*n-2 || k<0, 0, if(n==2 && k<=2, 1, if(k<n, T(n-1, k)+T(n, 2*n-1-k), T(n, 2*n-2-k))))) \\ _Paul D. Hanna_, Nov 12 2009

%Y Cf. A000957, A000958, A104629, A001558, A001559, A000108.

%K nonn,tabf

%O 0,11

%A _Philippe Deléham_, Nov 11 2009

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