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A055800 Array T read by rows: T(i,0)=1 for i >= 0; T(i,i)=0 for i >= 1; T(i,j)=Sum{T(i-2k,j-2k+1): k >= 1} for 1<=j<=i-1, where T(m,n) := 0 if m<0 or n<0. 0
1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 1, 1, 1, 2, 3, 4, 3, 1, 0, 1, 1, 1, 2, 3, 4, 3, 1, 0, 0, 1, 1, 1, 2, 3, 5, 7, 7, 4, 1, 0, 1, 1, 1, 2, 3, 5, 7, 7, 4, 1, 0, 0, 1, 1, 1, 2, 3, 5, 8, 12, 14, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,25

COMMENTS

T(i+j,j)=number of strings (s(1),...,s(m)) of nonnegative integers s(k) such that m<=i+1, s(m)=j and s(k)-s(k-1) is an odd positive integer for k=2,3,...,m.

T(i+j,j)=number of compositions of j consisting of at most i parts, all positive odd integers.

REFERENCES

C. Kimberling, Path-counting and Fibonacci numbers, Fib. Quart. 40 (4) (2002) 328-338, example 2A.

LINKS

Table of n, a(n) for n=0..87.

FORMULA

G.f. for k-th diagonal: (1-x^2-x*(x/(1-x^2))^k)/(1-x-x^2). - Vladeta Jovovic, Mar 10 2005

EXAMPLE

Rows: 1; 1,0; 1,1,0; 1,1,0,0; 1,1,1,1,0; ...

T(10,5) counts the strings 012345, 0125, 0145, 0345, 05.

T(10,5) counts the compositions 11111, 113, 131, 311, 5.

CROSSREFS

Row sums are powers of 2: 1, 1, 2, 2, 4, 4, 8, 8, 16, 16, ...

T(2n, n)=A000045(n) for n >= 1 (Fibonacci numbers).

Cf. A027926.

Sequence in context: A016385 A189996 A016390 * A060572 A163543 A180009

Adjacent sequences:  A055797 A055798 A055799 * A055801 A055802 A055803

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, May 28 2000

STATUS

approved

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Last modified January 17 06:41 EST 2019. Contains 319207 sequences. (Running on oeis4.)