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A194847 Write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives i values. 11
2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Each n >= 0 has a unique representation as n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0. This is the combinatorial number system of degree t = 3, where we get [A194847, A194848, A056558]. For degree t = 2 we get [A002024, A002262] and A138036.

REFERENCES

D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.

LINKS

Table of n, a(n) for n=0..123.

FORMULA

Equals A056556(n) + 2.

EXAMPLE

The i,j,k coordinates for n equal to 0 through 10 are:

0, [2, 1, 0]

1, [3, 1, 0]

2, [3, 2, 0]

3, [3, 2, 1]

4, [4, 1, 0]

5, [4, 2, 0]

6, [4, 2, 1]

7, [4, 3, 0]

8, [4, 3, 1]

9, [4, 3, 2]

10, [5, 1, 0]

MAPLE

# Given x and a list a, returns smallest i such that x >= a[i].

whereinlist:=proc(x, a)  local i:

if whattype(a) <> list then ERROR(`a not a list`); fi:

for i from 1 to nops(a) do if x < a[i] then break; fi; od:

RETURN(i-1); end:

t3:=[seq(binomial(n, 3), n=0..50)];

t2:=[seq(binomial(n, 2), n=0..50)];

t1:=[seq(binomial(n, 1), n=0..50)];

for n from 0 to 200 do

i3:=whereinlist(n, t3);

i2:=whereinlist(n-t3[i3], t2);

i1:=whereinlist(n-t3[i3]-t2[i2], t1);

L[n]:=[i3-1, i2-1, i1-1];

od:

[seq(L[n][1], n=0..200)];

CROSSREFS

The [i,j,k] values are [A194847, A194848, A056558], or equivalently [A056556+2, A056557+1, A056558]. See A194849 for the union list of triples.

Cf. also A002024, A002262, A138036.

Sequence in context: A081288 A130256 A103586 * A262070 A117806 A085423

Adjacent sequences:  A194844 A194845 A194846 * A194848 A194849 A194850

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 03 2011

STATUS

approved

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Last modified January 17 16:11 EST 2019. Contains 319235 sequences. (Running on oeis4.)