A123262 Fibonacci-tribonacci triangle.

0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 3, 0, 0, 0, 0, 2, 5, 0, 0, 0, 0, 0, 5, 8, 0, 0, 0, 0, 0, 1, 10, 13, 0, 0, 0, 0, 0, 0, 3, 20, 21, 0, 0, 0, 0, 0, 0, 0, 9, 38, 34, 0, 0, 0, 0, 0, 0, 0, 1, 22, 71, 55, 0, 0, 0, 0, 0, 0, 0, 0, 4, 51, 130, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 111, 235, 144

Offset

0,10

Comments

Or, skew Jacobsthal-Lucas triangle, read by rows.

Links

Table of n, a(n) for n=0..90.

Formula

T(n,k)=T(n-1,k-1)+T(n-2,k-2)+T(n-3,k-2), T(n,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n . T(n,n)= Fibonacci(n)=A000045(n) . Sum_{k, 0<=k<=n}T(n,k)=A000073(n+1), tribonacci numbers . Sum_{n, n>=k}T(n,k)=A001045(k), Jacobsthal sequence.

Example

Triangle begins:
.0;
.0, 1;
.0, 0, 1;
.0, 0, 0, 2;
.0, 0, 0, 1, 3;
.0, 0, 0, 0, 2, 5;
.0, 0, 0, 0, 0, 5, 8;
.0, 0, 0, 0, 0, 1, 10, 13;
.0, 0, 0, 0, 0, 0, 3, 20, 21;
.0, 0, 0, 0, 0, 0, 0, 9, 38, 34;
.0, 0, 0, 0, 0, 0, 0, 1, 22, 71, 55;
.0, 0, 0, 0, 0, 0, 0, 0, 4, 51, 130, 89;
.0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 111, 235, 144;

Crossrefs

Cf. A037027.

Sequence in context: A296167 A244233 A227345 * A191906 A371647 A187080

Adjacent sequences: A123259 A123260 A123261 * A123263 A123264 A123265

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 06 2006

Status

approved