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A119366 Number of rooted planar n-trees whose number of leaves is equal to 1 modulo 3. 3
0, 1, 1, 1, 2, 11, 51, 177, 519, 1513, 5042, 18866, 71270, 257974, 905425, 3193737, 11578842, 42930441, 159998493, 593445318, 2194106568, 8138471667, 30399156174, 114219616809, 430344635913, 1622777285682, 6125465491551 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n)+A119365(n)+A119367(n)=A000108(n).

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n)=sum{k=0..n, if(mod(n-k,3)=1, (1/n)*C(n,k)*C(n,k+1), 0)}

a(0)=0, a(n)=sum{k=0..floor(n/3), (1/n)*C(n,3k+1)C(n,3k)},n>0; - Paul Barry, Jan 25 2007

MAPLE

A119366 := proc(n)

    if n = 0 then

        0;

    else

        add(binomial(n, 3*k+1)*binomial(n, 3*k), k=0..n/3) ;

        %/n ;

    end if;

end proc: # R. J. Mathar, Dec 02 2014

CROSSREFS

Sequence in context: A137960 A018933 A116586 * A034574 A054665 A134963

Adjacent sequences:  A119363 A119364 A119365 * A119367 A119368 A119369

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 16 2006

STATUS

approved

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Last modified August 10 02:28 EDT 2020. Contains 336367 sequences. (Running on oeis4.)