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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

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: A035148 A155077 A170968 * A090787 A229707 A262680

Adjacent sequences:  A114111 A114112 A114113 * A114115 A114116 A114117

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 13 2005

STATUS

approved

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Last modified July 17 09:09 EDT 2019. Contains 325099 sequences. (Running on oeis4.)