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A050143 Array T by antidiagonals: T(i,j)=Sum{T(h,k): 0<=h<=i-1, 0<=k<=j}, T(i,0)=1 for i >= 0, T(0,j)=0 for j >= 1. 9
1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 4, 7, 1, 0, 1, 5, 12, 15, 1, 0, 1, 6, 18, 32, 31, 1, 0, 1, 7, 25, 56, 80, 63, 1, 0, 1, 8, 33, 88, 160, 192, 127, 1, 0, 1, 9, 42, 129, 280, 432, 448, 255, 1, 0, 1, 10, 52, 180, 450, 832, 1120, 1024, 511, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Formatted as a triangular array with offset (0,8), it is [0, 1, 0, -1, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 1, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe Deléham, Nov 05 2006

The sum of the first two columns gives the powers of 2, that is, Sum[T(i,j),j=0..1] = 2^i, i>=0. On the other hand, for i>=1 and j>=2, T(i,j) is the number of lattice paths of i-1 upsteps (1,1) and j-1 downsteps (1,-1) in which each downstep-free vertex is colored red or blue. A downstep-free vertex is one not incident with a downstep. For example, dots indicate the downstep-free vertices in the path .U.U.UDU.UDDU., and with i=j=2, T(2,2) = 4 counts UD, *UD, DU, DU*, where asterisks indicate the red vertices. - David Callan, Aug 27 2011

LINKS

Table of n, a(n) for n=1..68.

EXAMPLE

Antidiagonals, each starting on top row: {1}; {0,1}; {0,1,1}; {0,1,3,1}; ...

CROSSREFS

Antidiagonal sums are odd-indexed Fibonacci numbers (A001519).

Signed alternating antidiagonal sums are F(n)-2, as in A001911.

T(n, 1)=-1+2^n=A000225(n). T(n+2, 2)=4*A001792(n). Cf. A050147, A050148.

Cf. A055807 (mirror array).

Sequence in context: A264435 A085391 A280880 * A103495 A261699 A285574

Adjacent sequences:  A050140 A050141 A050142 * A050144 A050145 A050146

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)