A368563 - OEIS

A368563

Table read by downward antidiagonals: ranked maximum r likelihood of the number of distinguishable marbles in an urn if repeated random sampling of one marble with replacement yields n different marbles before the first repeated marble.

1, 1, 2, 1, 3, 5, 1, 4, 4, 8, 1, 5, 6, 9, 13, 1, 6, 7, 10, 14, 19, 1, 7, 8, 7, 12, 18, 25, 1, 8, 9, 11, 15, 20, 26, 33, 1, 9, 3, 12, 11, 17, 27, 34, 42, 1, 10, 10, 6, 16, 21, 24, 32, 41, 51, 1, 11, 11, 13, 17, 22, 28, 35, 43, 52, 62, 1, 12, 12, 14, 10, 16, 23

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..73.

EXAMPLE

Table T(n,r) begins:

n\r | 1 2 3 4 5 6 7 8 9 10 11

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

1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

2 | 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

3 | 5, 4, 6, 7, 8, 9, 3, 10, 11, 12, 13

4 | 8, 9, 10, 7, 11, 12, 6, 13, 14, 15, 16

5 | 13, 14, 12, 15, 11, 16, 17, 10, 18, 19, 20

6 | 19, 18, 20, 17, 21, 22, 16, 23, 24, 15, 25

7 | 25, 26, 27, 24, 28, 23, 29, 22, 30, 31, 21

8 | 33, 34, 32, 35, 31, 36, 30, 37, 38, 29, 39

9 | 42, 41, 43, 40, 44, 39, 45, 46, 38, 47, 37

10 | 51, 52, 50, 53, 54, 49, 55, 48, 56, 47, 57

11 | 62, 63, 61, 64, 60, 65, 59, 66, 58, 67, 57

12 | 74, 73, 75, 72, 76, 71, 77, 70, 78, 79, 69

13 | 86, 87, 85, 88, 84, 89, 90, 83, 91, 82, 92

MATHEMATICA

l[n_, r_] := l[n, r] = Table[Product[(M - i + 1)/M, {i, 2, n}]*n/M, {M, 2, n^2*r}];

T[1, r_] = 1; T[n_, r_] := T[n, r] = Module[{pos}, pos = Position[l[n, r], RankedMax[l[n, r], r]]; If[Length[pos] == 0, -1, pos[[1, 1]] + 1]];

(*Table*)Table[T[n, r], {n, 1, 13}, {r, 1, 11}] // TableForm

(*Data*)Table[T[n, r - n + 1], {r, 1, 12}, {n, 1, r}] // Flatten

CROSSREFS

Cf. A111097 (column 1).

Cf. A000012 (row 1), A000027 (row 2).

Sequence in context: A210563 A236311 A347773 * A093412 A119355 A076110

Adjacent sequences: A368560 A368561 A368562 * A368564 A368565 A368566

KEYWORD

nonn,tabl

AUTHOR

Robert P. P. McKone, Dec 30 2023

STATUS

approved