A114114 An invertible partition matrix.

1, 1, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1

Offset

0,5

Comments

Row sums are n+1, A000027. Diagonal sums are 1,1,1,2,2,2,3,3,3,.... or A008620. Inverse is A114115. Product with first difference matrix (1-x,x) is A114117.

Links

Table of n, a(n) for n=0..90.

Formula

Number triangle T(n, k)=sum{j=0..n, C(floor((n+j)/2), k)C(k, floor((n+j)/2))}.

Example

Triangle begins
1.................=1
1,1...............=2
0,2,1.............=3
0,1,2,1...........=4
0,0,2,2,1.........=5
0,0,1,2,2,1.......=6
0,0,0,2,2,2,1.....=7
0,0,0,1,2,2,2,1...=8

Crossrefs

Sequence in context: A155077 A358074 A170968 * A090787 A351559 A229707

Adjacent sequences: A114111 A114112 A114113 * A114115 A114116 A114117

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 13 2005

Status

approved