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A055794 Array T read by rows: T(i,0)=1 for i >= 0; T(i,i)=0 for i=0,1,2,3; T(i,i)=0 for i >= 4; T(i,j)=T(i-1,j)+T(i-2,j-1) for 1<=j<=i-1. 5
1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 4, 2, 0, 1, 5, 7, 4, 1, 0, 1, 6, 11, 8, 3, 0, 0, 1, 7, 16, 15, 7, 1, 0, 0, 1, 8, 22, 26, 15, 4, 0, 0, 0, 1, 9, 29, 42, 30, 11, 1, 0, 0, 0, 1, 10, 37, 64, 56, 26, 5, 0, 0, 0, 0, 1, 11, 46, 93, 98, 56, 16, 1, 0, 0, 0, 0, 1, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(i+j,j)=number of strings (s(1),...,s(i+1)) of nonnegative integers s(k) such that 0<=s(k)-s(k-1)<=1 for k=2,3,...,i+1 and s(i+1)=j.

T(i+j,j)=number of compositions of j consisting of i parts, all of in {0,1}.

LINKS

Table of n, a(n) for n=0..79.

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

EXAMPLE

Triangle begins:

  1;

  1,1;

  1,2,1;

  1,3,2,1;

  1,4,4,2,0;

  ...

T(7,4) counts the strings 3334, 3344, 3444, 2234, 2334, 2344, 1234.

T(7,4) counts the compositions 001, 010, 100, 011, 101, 110, 111.

CROSSREFS

Row sums: A000032 (Lucas numbers, 1, 2, 4, 7, 11, 18, ...).

T(2n, n)=A000125(n) (Cake numbers, 1, 2, 4, 8, 15, 26, ...).

T(2n+2, n)=A027660(n).

Sequence in context: A278427 A077592 A194005 * A092905 A052509 A172119

Adjacent sequences:  A055791 A055792 A055793 * A055795 A055796 A055797

KEYWORD

nonn,tabl,changed

AUTHOR

Clark Kimberling, May 28 2000

STATUS

approved

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)