1,3

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)=1.

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

If 1 2 1, then a(3)=1+1=2.

If 1 4 2 1, then a(4)=1+2=3.

If 1 8 4 2 1, then a(5)=1+4+1=6.

If 1 16 8 4 2 1, then a(6)=1+8+2=11.

If 1 31 17 8 4 2 1, then a(7)=1+16+4+1=22.

If 1 60 35 17 8 4 2 1, then a(8)=1+31+8+2=42.

If 1 116 72 35 17 8 4 2 1, then a(9)=1+60+17+4+1=82.

If 1 224 148 72 35 17 8 4 2 1, then a(10)=1+116+35+8+2=162.

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

a(11)=1+224+72+17+4+1=319 etc.

Cf. A140998.

Sequence in context: A018613 A036589 A123341 this_sequence A043328 A002083 A124973

Adjacent sequences: A141069 A141070 A141071 this_sequence A141073 A141074 A141075

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