1,1

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, Pascal-like triangles and Pascal's triangle are connected by the recurrence relation ...

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

If 1

1 1

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

If 1 4 2 1

1 8 4 2 1

1 16 8 4 2 1

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

If 1 60 35 17 8 4 2 1

1 116 72 35 17 8 4 2 1

1 224 148 72 35 17 8 4 2 1

1 432 303 149 72 35 17 8 4 2 1, then a(4)=149, etc.

Cf. A140998.

Sequence in context: A132146 A139827 A063118 this_sequence A162622 A078164 A060387

Adjacent sequences: A141065 A141066 A141067 this_sequence A141069 A141070 A141071

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