A060162 Triangle T(n,m) with T(n,m)=T(n-1,|m-1|)+T(n-1,m)+T(n-1,m+1)-2T(n-2,m) and T(0,0)=1.

1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 4, 4, 1, 7, 9, 6, 7, 5, 1, 15, 14, 14, 10, 11, 6, 1, 29, 25, 26, 21, 17, 16, 7, 1, 49, 52, 44, 44, 32, 28, 22, 8, 1, 95, 95, 88, 78, 70, 50, 44, 29, 9, 1, 187, 174, 173, 148, 134, 108, 79, 66, 37, 10, 1, 345, 344, 319, 299, 250, 221, 165, 124, 95

Offset

0,5

References

B. A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8. English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see p. 44.

Links

Table of n, a(n) for n=0..74.

Example

T(4,3)=T(3,2)+T(3,3)+T(3,4)-2*T(2,3)=3+1+0-2*0=4. T(5,0)=T(4,1)+T(4,0)+T(4,1)-2*T(3,0)=4+5+4-2*3=7. Rows are: (1), (1,1), (1,2,1), (3,2,3,1), (5,4,4,4,1), ...

Crossrefs

Half of a generalized Pascal triangle of order 3: A059780. Diagonals include A000012, A000027, A000124, A060163.

Sequence in context: A335421 A263017 A245328 * A026730 A318691 A075256

Adjacent sequences: A060159 A060160 A060161 * A060163 A060164 A060165

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Mar 13 2001

Status

approved