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A107110 Square array by antidiagonals where T(n,k) is the number of partitions of k into no more than n parts each no more than n. Visible version of A063746. 1
1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 3, 2, 1, 1, 0, 0, 0, 3, 3, 2, 1, 1, 0, 0, 0, 3, 5, 3, 2, 1, 1, 0, 0, 0, 3, 5, 5, 3, 2, 1, 1, 0, 0, 0, 2, 7, 7, 5, 3, 2, 1, 1, 0, 0, 0, 1, 7, 9, 7, 5, 3, 2, 1, 1, 0, 0, 0, 1, 8, 11, 11, 7, 5, 3, 2, 1, 1, 0, 0, 0, 0, 7, 14, 13, 11, 7, 5, 3, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Table of n, a(n) for n=0..102.

Henry Bottomley, Partition and composition calculator.

FORMULA

See A063746 for formulas. T(n, k)=A000041(k) if n>=k. T(n, k)=T(n, n^2-k). T(n, [n^2/2])=A029895(n); T(2n, 2n^2)=A063074(n). Row sums are A000984.

EXAMPLE

Rows start 1,0,0,0,...; 1,1,0,0,0,...; 1,1,2,1,1,0,0,0,...; 1,1,2,3,3,3,3,2,1,1,0,0,0,...; 1,1,2,3,5,5,7,7,8,7,7,5,5,3,2,1,1,0,0,0,...; etc.

T(4,6)=7 since 6 can be written seven ways with no more than 4 parts each no more than 4: 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, or 2+2+1+1.

CROSSREFS

Cf. A063746. Fifth row is A102422.

Sequence in context: A134404 A249609 A232442 * A061197 A196346 A261884

Adjacent sequences:  A107107 A107108 A107109 * A107111 A107112 A107113

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, May 12 2005

STATUS

approved

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Last modified November 18 09:55 EST 2019. Contains 329261 sequences. (Running on oeis4.)