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A055215 A path-counting array, read by rows: T(i,j)=number of paths from (0,0) to (i-j,j) using steps (1 unit right and 1 unit up) or (1 unit right and 2 units up). 1
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 4, 2, 1, 1, 1, 2, 3, 5, 4, 2, 1, 1, 1, 2, 3, 5, 7, 4, 2, 1, 1, 1, 2, 3, 5, 8, 8, 4, 2, 1, 1, 1, 2, 3, 5, 8, 12, 8, 4, 2, 1, 1, 1, 2, 3, 5, 8, 13, 15, 8, 4, 2, 1, 1, 1, 2, 3, 5, 8, 13, 20, 16 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

If m >= 1 and n >= 2, then T(m+n-1,m) is the number of strings (s(1),s(2),...,s(n)) of nonnegative integers satisfying s(n)=m and 1<=s(k)-s(k-1)<=2 for k=2,3,...,n.

LINKS

Table of n, a(n) for n=1..87.

C. Kimberling, Path-counting and Fibonacci numbers, Fib. Quart. 40 (4) (2002) 328-338, Example 1D.

FORMULA

T(i, 0)=T(i, i)=1 for i >= 0; T(i, 1)=1 for i >= 1; T(i, j)=T(i-2, j-1)+T(i-3, j-2) for 2<=j<=i-1, i >= 3.

EXAMPLE

7=T(8,5) counts these strings: 0135, 0235, 0245, 1235, 1245, 1345, 2345.

Rows: {1}; {1,1}; {1,1,1}; {1,1,2,1}; {1,1,2,2,1}; ...

CROSSREFS

T(2n, n)=A000045(n+1), the Fibonacci numbers.

Sequence in context: A241918 A276317 A289944 * A239550 A058398 A091499

Adjacent sequences:  A055212 A055213 A055214 * A055216 A055217 A055218

KEYWORD

nonn,tabl,walk

AUTHOR

Clark Kimberling, May 07 2000

STATUS

approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)