1,2

Pascal-like triangle with index of asymmetry (y=1) 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, k)=G(n+1, k-1)+G(n+1, k)+G(n+2, k) for k:=1..(n+1).

Pascal-like triangle with index of asymmetry(y=1) 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, k)=G(n+1,

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

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

Pascal-like triangle (y=1, z=0) begins:

If 1, then a(1)=1.

If 1 1

1 2 1

1 4 2 1, then a(2)=4.

If 1 7 5 2 1

1 12 11 5 2 1, then a(3)=12.

If 1 20 23 12 5 2 1, then a(4)=20.

If 1 33 46 28 12 5 2 1, then a(5)=28, a(6)=33, a(7)=46.

If 1 54 89 63 29 12 5 2 1, then a(8)=54, a(9)=63.

If 1 88 168 137 69 29 12 5 2 1, then a(10)=69 and

1 143 311 289 161 70 29 12 5 2 1, then a(11)=70, a(12)=88,

a(13)=143, a(14)=161.

If 1 232 567 594 367 168 70 29 12 5 2 1, then a(15)=168,...

ets.

Cf. A140998.

Sequence in context: A100717 A030387 A043437 this_sequence A031065 A017113 A081770

Adjacent sequences: A141062 A141063 A141064 this_sequence A141066 A141067 A141068

nonn,uned

Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 14 2008

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