1,7

Pascal-like triangle with index of asymmetry (y=3) and index of

obliqueness (z=0) read by rows with recurence G(n, k): G(n, 0)=G(n+1,

n+1)=1, G(n+2, n+1)=2, G(n+3, n+1)=4, G(n+4, n+1)=8, G(n+5, k)=G(n+1,

k-1)+G(n+1,

k)+G(n+2, k)+G(n+3, k)+G(n+4, k) for k:=1..(n+1).

Pascal-like triangle with index of asymmetry(y=3) and index of obliqueness

(z=1) read by rows with recurence G(n, k): G(n, n)=G(n+1, 0)=1, G(n+2,

1)=2, G(n+3, 2)=4, G(n+4, 3)=8, G(n+5, k)=G(n+1, k-3)+G(n+1, k-4)+G(n+2,

k-3)+G(n+3,

k-2)+G(n+4, k-1) for k=4..(n+4).

Juri-Stepan Gerasimov, Stepan's triangles and Pascal's triangle are connected by the recurrence relation ...

Pascal-like triangle (y=3, z=0) begins:

If 1, then a(1)=0.

If 1 1, then a(2)=0.

If 1 2 1, then prime 2 and a(3)=1.

If 1 4 2 1, then prime 2 and a(4)=1.

If 1 8 4 2 1, then prime 2 and a(5)=1.

If 1 16 8 4 2 1, then prime 2 and a(6)=1.

If 1 31 17 8 4 2 1, then primes 2, 17, 31 and a(7)=3.

If 1 60 35 17 8 4 2 1, then primes 2, 17 and a(8)=2.

If 1 116 72 35 17 8 4 2 1, then primes 2, 17 and a(9)=2.

If 1 224 148 72 35 17 8 4 2 1, then primes 2, 17 and

a(10)=2.

If 1 432 303 149 72 35 17 8 4 2 1, then primes 2, 17, 149

and a(11)=3, etc.

Cf. A140998.

Sequence in context: A085034 A119323 A102299 this_sequence A163751 A067279 A096101

Adjacent sequences: A141067 A141068 A141069 this_sequence A141071 A141072 A141073

nonn,uned

Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 16 2008

Partially edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 18 2008