A194848 Write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives j values.

1, 1, 2, 2, 1, 2, 2, 3, 3, 3, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 1, 2, 2

Offset

0,3

Comments

See A194847.

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..122.

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 22.

Formula

Equals A056557(n) + 1.

Maple

See A194847.

Prog

(Python)
from math import isqrt, comb
from sympy import integer_nthroot
def A194848(n): return (k:=isqrt(r:=n+1-comb((m:=integer_nthroot(6*(n+1), 3)[0])-(n<comb(m+2, 3))+2, 3)<<1))+((r<<2)>(k<<2)*(k+1)+1) # Chai Wah Wu, Nov 04 2024

Crossrefs

The [i,j,k] values are [A194847, A194848, A056558].

Sequence in context: A014420 A029289 A181834 * A289497 A029328 A109831

Adjacent sequences: A194845 A194846 A194847 * A194849 A194850 A194851

Keyword

nonn

Author

N. J. A. Sloane, Sep 03 2011

Status

approved