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A156869 Triangle read by rows: T(n,k) = number of nondecreasing sequences of n positive integers with reciprocals adding up to k (1 <= k <= n). 6
1, 1, 1, 3, 1, 1, 14, 4, 1, 1, 147, 17, 4, 1, 1, 3462, 164, 18, 4, 1, 1, 294314, 3627, 167, 18, 4, 1, 1, 159330691, 297976, 3644, 168, 18, 4, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Conjecture: T(2n + m, n + m) = T(2n, n) ( = A156870(n) ) if and only if m >= 0.

Yes, the diagonals are constant for n <= 2k. Any such sequence must have at least one 1; remove that 1, and you get a sequence for n-1,k-1. - Franklin T. Adams-Watters, Feb 20 2009

The next term will be a(37) = A002966(9). - M. F. Hasler, Feb 20 2009

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

Triangle begins:

n=1:      1

n=2:      1,    1

n=3:      3,    1,   1

n=4:     14,    4,   1,  1

n=5:    147,   17,   4,  1, 1

n=6:   3462,  164,  18,  4, 1, 1

n=7: 294314, 3627, 167, 18, 4, 1, 1

For n = 4 and k = 2, the T(4, 2) = 4 sequences are (1, 2, 3, 6), (1, 2, 4, 4), (1, 3, 3, 3) and (2, 2, 2, 2) because 1/1 + 1/2 + 1/3 + 1/6 = 1/1 + 1/2 + 1/4 + 1/4 = 1/1 + 1/3 + 1/3 + 1/3 = 1/2 + 1/2 + 1/2 + 1/2 = 2.

PROG

(PARI) { A156869(n, k, m=1) = n==1 & return(numerator(k)==1 & denominator(k)>=m); sum( i=max(m, 1\k+1), n\k, A156869(n-1, k-1/i, i)); } \\ M. F. Hasler, Feb 20 2009

CROSSREFS

Cf. A002966 (column k=1), A156871 (row sums), A280519, A280520.

T(2n, n) = A156870(n).

Sequence in context: A055154 A015112 A174690 * A153090 A203002 A073483

Adjacent sequences:  A156866 A156867 A156868 * A156870 A156871 A156872

KEYWORD

more,nonn,tabl

AUTHOR

Jens Voß, Feb 17 2009

EXTENSIONS

a(21)-a(36) from M. F. Hasler, Feb 20 2009

STATUS

approved

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Last modified September 24 18:54 EDT 2017. Contains 292433 sequences.