1,1

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

1 1

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

If 1 4 2 1

1 8 4 2 1

1 15 9 4 2 1

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

If 1 52 40 19 9 4 2 1

1 96 83 41 19 9 4 2 1, then a(3)=41 and a(4)=83.

If 1 177 170 88 41 19 9 4 2 1

1 326 345 188 88 41 19 9 4 2 1

1 600 694 400 189 88 41 19 9 4 2 1

1 1104 1386 846 406 189 88 41 19 9 4 2 1

1 2031 2751 1779 871 406 189 88 41 19 9 4 2 1

1 3736, 5431, 3719, 1866, 872, 406, 189, 88, 41, 19, 9, 4, 2,

1 ets.

Cf. A140998.

Sequence in context: A075682 A062587 A109946 this_sequence A140560 A031911 A136685

Adjacent sequences: A141064 A141065 A141066 this_sequence A141068 A141069 A141070

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