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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
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, 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, 111, 54, 21, 6, 1, 0, 0, 1, 7, 28, 82, 193, 379, 622, 808, 622, 379, 193, 82, 28, 7, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..80.

EXAMPLE

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 ; ...

PROG

(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

CROSSREFS

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

Sequence in context: A319573 A178904 A017858 * A119369 A122445 A189511

Adjacent sequences:  A167766 A167767 A167768 * A167770 A167771 A167772

KEYWORD

nonn,tabf

AUTHOR

Philippe Deléham, Nov 11 2009

STATUS

approved

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Last modified August 25 16:14 EDT 2019. Contains 326324 sequences. (Running on oeis4.)