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A056556 First tetrahedral co-ordinate; repeat m (m+1)*(m+2)/2 times. 15
0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

If {(X,Y,Z)} are triples of nonnegative integers with X>=Y>=Z ordered by X, Y and Z, then X=A056556(n), Y=A056557(n) and Z=A056558(n)

From Gus Wiseman, Jul 03 2019: (Start)

Also the maximum number of distinct multiplicities among integer partitions of n. For example, random partitions of 56 realizing each number of distinct multiplicities are:

  1: (24,17,6,5,3,1)

  2: (10,9,9,5,5,4,4,3,3,2,1,1)

  3: (6,5,5,5,4,4,4,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)

  4: (28,5,5,3,3,3,2,2,1,1,1,1,1)

  5: (13,4,4,4,4,4,3,3,3,2,2,2,2,2,2,1,1)

  6: (6,5,5,4,4,4,3,3,3,3,2,2,2,2,2,1,1,1,1,1,1)

The maximum number of distinct multiplicities is 6, so a(56) = 6.

(End)

LINKS

Table of n, a(n) for n=0..104.

FORMULA

a(n)=floor[x] where x is the (largest real) solution to x^3+3x^2+2x-6n=0; a(A000292(n))=n+1

a(n+1) = a(n)==A056558(n) ? a(n)+1 : a(n) - Graeme McRae, Jan 09 2007

MATHEMATICA

Table[Table[m, {(m+1)(m+2)/2}], {m, 0, 7}] // Flatten (* Jean-Fran├žois Alcover, Feb 28 2019 *)

PROG

(PARI) a(n)=my(t=polrootsreal(x^3+3*x^2+2*x-6*n)); t[#t]\1 \\ Charles R Greathouse IV, Feb 22 2017

CROSSREFS

Cf. A000292, A003056, A056557, A056558, A056559, A056560.

See also A194847.

Cf. A088880, A088881, A116608, A325242.

Sequence in context: A220104 A191228 A286103 * A111651 A151982 A259361

Adjacent sequences:  A056553 A056554 A056555 * A056557 A056558 A056559

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jun 26 2000

STATUS

approved

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Last modified October 14 15:14 EDT 2019. Contains 328019 sequences. (Running on oeis4.)