1,2

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

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

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

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

Pascal-like triangle (y=2, 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 8 4 2 1, then a(3)=8.

If 1 15 9 4 2 1, then a(4)=12 and a(5)=15.

If 1 28 19 9 4 2 1, then a(6)=28.

If 1 52 40 19 9 4 2 1, then a(7)=40 and a(8)=52.

If 1 96 83 41 19 9 4 2 1

1 177 170 88 41 19 9 4 2 1, then a(9)=88, a(10)=96,

a(11)=170, a(12)=177.

If 1 326 345 188 88 41 19 9 4 2 1

1 600 694 400 189 88 41 19 9 4 2 1, then a(13)=188,

a(14)=189, a(15)=326, a(16)=345, a(17)=400, ets.

Cf. A140998.

Adjacent sequences: A141063 A141064 A141065 this_sequence A141067 A141068 A141069

Sequence in context: A161542 A131195 A020217 this_sequence A018196 A072103 A004756

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