A365213 - OEIS

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A365213

Triangle T(n, k), n >= 0, k = 0..n, read by rows: let's consider a triangle of initially empty glasses of equal volume, G(n, k), n >= 0, k = 0..n; when water is poured into one of the glasses, say G(n, k), it flows into that glass until it's full, and then the excess overflows equally into G(n+1, k) and G(n+1, k+1); let V(n, k) be the minimum volume of water to be poured into G(0, 0) so as to fill G(n, k) completely; T(n, k) is the denominator of V(n, k) / V(0, 0).

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 3, 1, 3, 1, 1, 1, 5, 5, 1, 1, 1, 5, 5, 5, 5, 5, 1, 1, 5, 1, 17, 17, 1, 5, 1, 1, 1, 5, 25, 17, 25, 5, 1, 1, 1, 7, 27, 55, 3, 3, 55, 27, 7, 1, 1, 2, 11, 75, 9, 25, 9, 75, 11, 2, 1, 1, 9, 35, 55, 50, 215, 215, 50, 55, 35, 9, 1

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

OFFSET

0,8

COMMENTS

See A365212 for the numerators.

LINKS

Table of n, a(n) for n=0..77.

Rémy Sigrist, PARI program

FORMULA

T(n, k) = T(n, n - k).

T(n, 0) = 1.

EXAMPLE

Triangle T(n, k) begins:

1 1

1 1 1

1 3 3 1

1 3 1 3 1

1 1 5 5 1 1

1 5 5 5 5 5 1

1 5 1 17 17 1 5 1

1 1 5 25 17 25 5 1 1

Triangle V(n, k) / V(0, 0) begins:

3 3

7 5 7

15 25/3 25/3 15

31 41/3 11 41/3 31

63 22 77/5 77/5 22 63

127 183/5 109/5 93/5 109/5 183/5 127

255 311/5 31 403/17 403/17 31 311/5 255

511 105 226/5 779/25 467/17 779/25 226/5 105 511

PROG

(PARI) See Links section.

CROSSREFS

Cf. A365212 (numerators).

Sequence in context: A125300 A371741 A303992 * A126717 A124039 A379488

Adjacent sequences: A365210 A365211 A365212 * A365214 A365215 A365216

KEYWORD

nonn,frac,tabl

AUTHOR

Rémy Sigrist, Aug 26 2023

STATUS

approved