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A114114 An invertible partition matrix. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Nov 13 2005
STATUS
approved

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Last modified April 17 07:13 EDT 2024. Contains 371756 sequences. (Running on oeis4.)