A391661 - OEIS

A391661

Square array read by antidiagonals: T(n,k) is the Kruskal-Macaulay function L_n of degree n evaluated at k.

0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 6, 1, 0, 0, 0, 10, 1, 0, 0, 0, 0, 15, 2, 1, 0, 0, 0, 0, 21, 4, 1, 0, 0, 0, 0, 0, 28, 4, 1, 1, 0, 0, 0, 0, 0, 36, 5, 2, 1, 0, 0, 0, 0, 0, 0, 45, 7, 2, 1, 1, 0, 0, 0, 0, 0, 0, 55, 10, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 66, 10, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0

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OFFSET

1,7

COMMENTS

T(n,k) is the maximum number of cells of a directed animal with perimeter k in the (n+1)-dimensional integer lattice.

REFERENCES

Donald E. Knuth, The Art of Computer Programming, Vol. 4A (Combinatorial Algorithms, Part 1), Addison-Wesley, 2011. See Table 3 on page 375 in Section 7.2.1.3.

LINKS

Table of n, a(n) for n=1..91.

FORMULA

T(n,k) = max {m; A391660(n+1,m)<=k}.

EXAMPLE

Array begins:

n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

---+--------------------------------------------------------------------

1 | 0 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190

2 | 0 0 0 1 1 2 4 4 5 7 10 10 11 13 16 20 20 21 23 26 30

3 | 0 0 0 0 1 1 1 2 2 3 5 5 5 6 6 7 9 9 10 12 15

4 | 0 0 0 0 0 1 1 1 1 2 2 2 3 3 4 6 6 6 6 7 7