0,6

Skew triangle associated with the Fibonacci numbers.

Sum_{k, 0<=k<=n}T(n,k)=A011782(n) . Sum_{n,n>=k}T(n,k)=A001333(k) . T(n,k)=0 if k<0 or if k>n, T(0,0)=1, T(2,1)=0, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-2,k-2) . T(n,n)=Fibonacci(n+1)=A000045(n+1).

Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A011782(n), A133592(n), A133594(n), A133642(n), A133646(n), A133678(n), A133679(n), A133680(n), A133681(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2008

Triangle begins:

.1;

.0, 1;

.0, 0, 2;

.0, 0, 1, 3;

.0, 0, 0, 3, 5;

.0, 0, 0, 1, 7, 8;

.0, 0, 0, 0, 4, 15, 13;

.0, 0, 0, 0, 1, 12, 30, 21;

.0, 0, 0, 0, 0, 5, 31, 58, 34;

.0, 0, 0, 0, 0, 1, 18, 73, 109, 55;

.0, 0, 0, 0, 0, 0, 6, 54, 162, 201, 89;

.0, 0, 0, 0, 0, 0, 1, 25, 145, 344, 365, 144;

.0, 0, 0, 0, 0, 0, 0, 7, 85, 361, 707, 655, 233;

Cf. A055830 (another version).

Sequence in context: A146164 A051510 A153036 this_sequence A116489 A166373 A056885

Adjacent sequences: A122947 A122948 A122949 this_sequence A122951 A122952 A122953

nonn,tabl

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 25 2006