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A096568 By rows, array T(n,k)=number of compositions of n with first part k and no equal adjacent parts. 6
1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 2, 1, 1, 1, 5, 4, 2, 1, 1, 1, 9, 5, 3, 3, 1, 1, 1, 14, 10, 6, 3, 3, 1, 1, 1, 25, 18, 12, 6, 4, 3, 1, 1, 1, 46, 29, 20, 13, 6, 4, 3, 1, 1, 1, 78, 53, 33, 20, 13, 7, 4, 3, 1, 1, 1, 136, 95, 59, 36, 22, 13, 7, 4, 3, 1, 1, 1, 242, 161, 104, 65, 36, 22, 14, 7, 4, 3, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row sums are the Carlitz sequence, A003242.

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..1035 (rows 1..45, flattened)

FORMULA

Define s(0)=1, T(1, 1)=1 and T(i, j)=0 for j>i. For n>=2 and 1<=k<=n, define s(n)=T(n, 1)+T(n, 2)+...+T(n, n) and T(n, k)=s(n-k)-T(n-k, k).

EXAMPLE

Triangle starts

01: 1,

02: 0, 1,

03: 1, 1, 1,

04: 2, 0, 1, 1,

05: 2, 2, 1, 1, 1,

06: 5, 4, 2, 1, 1, 1,

07: 9, 5, 3, 3, 1, 1, 1,

08: 14, 10, 6, 3, 3, 1, 1, 1,

09: 25, 18, 12, 6, 4, 3, 1, 1, 1,

10: 46, 29, 20, 13, 6, 4, 3, 1, 1, 1,

11: 78, 53, 33, 20, 13, 7, 4, 3, 1, 1, 1,

12: 136, 95, 59, 36, 22, 13, 7, 4, 3, 1, 1, 1,

13: 242, 161, 104, 65, 36, 22, 14, 7, 4, 3, 1, 1, 1,

14: 419, 283, 181, 111, 67, 38, 22, 14, 7, 4, 3, 1, 1, 1,

15: 733, 500, 319, 194, 118, 68, 38, 23, 14, 7, 4, 3, 1, 1, 1,

16: 1291, 869, 557, 342, 201, 120, 70, 38, 23, 14, 7, 4, 3, 1, 1, 1,

...

T(6,1)=5 counts the compositions 1+2+1+2, 1+2+3, 1+3+2, 1+4+1, 1+5.

PROG

(PARI)

R=20;

M=matrix(R, R);

T(n, k) = if (n==0, k==0, if (k==0, n==0, M[n, k] ) );

{ for (n=1, R,

    for(k=1, n,

        M[n, k] = sum(j=0, n, T(n-k, j)) - T(n-k, k);

    );

); }

for (n=1, R, for(k=1, n, print1(M[n, k], ", ") ); );

\\ Joerg Arndt, May 21 2013

CROSSREFS

Cf. A003242, A096569, A096570, A096571, A096572.

Sequence in context: A118198 A290885 A059881 * A025862 A004540 A089614

Adjacent sequences:  A096565 A096566 A096567 * A096569 A096570 A096571

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 27 2004

EXTENSIONS

Corrected by Joerg Arndt, May 21 2013

STATUS

approved

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Last modified November 21 11:01 EST 2018. Contains 317447 sequences. (Running on oeis4.)