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A138036 Write n = C(i,2)+C(j,1) with i>j>=0; let L[n] = [i,j]; sequence gives list of pairs L[n], n >= 0. 2
1, 0, 2, 0, 2, 1, 3, 0, 3, 1, 3, 2, 4, 0, 4, 1, 4, 2, 4, 3, 5, 0, 5, 1, 5, 2, 5, 3, 5, 4, 6, 0, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 7, 0, 7, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 8, 0, 8, 1, 8, 2, 8, 3, 8, 4, 8, 5, 8, 6, 8, 7, 9, 0, 9, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9, 8, 10, 0, 10, 1, 10, 2, 10, 3, 10, 4, 10, 5, 10, 6, 10, 7, 10, 8, 10, 9, 11, 0, 11, 1, 11, 2, 11, 3, 11, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Each n >= 0 has a unique representation as n = C(i,2)+C(j,1) with i>j>=0. This is the combinatorial number system of degree t = 2. The i values are A002024, the j values A002262.

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..119.

EXAMPLE

The pairs L[0] through L[10] are

[1, 0]

[2, 0]

[2, 1]

[3, 0]

[3, 1]

[3, 2]

[4, 0]

[4, 1]

[4, 2]

[4, 3]

[5, 0]

PROG

(Sage)

def A138036_list(len):

    i, j = 0, 1

    L = [1, 0]

    for _ in range(len):

        i += 1

        if i == j:

            j += 1

            i = 0

        L.append(j)

        L.append(i)

    return L

A138036_list(47) # Peter Luschny, May 18 2015

CROSSREFS

Cf. A002024, A002262. See A194847 for degree t=3.

Sequence in context: A061986 A127185 A159780 * A055136 A074397 A082023

Adjacent sequences:  A138033 A138034 A138035 * A138037 A138038 A138039

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Sep 04 2011

STATUS

approved

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Last modified August 21 11:42 EDT 2017. Contains 290864 sequences.