A014369 a(n) = bcd, where n = C(b,3)+C(c,2)+C(d,1), b>c>d>=0.

310, 320, 321, 410, 420, 421, 430, 431, 432, 510, 520, 521, 530, 531, 532, 540, 541, 542, 543, 610, 620, 621, 630, 631, 632, 640, 641, 642, 643, 650, 651, 652, 653, 654, 710, 720, 721, 730, 731, 732, 740, 741, 742, 743, 750, 751, 752, 753

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

In the definition bcd means concatenation not multiplication. - Sean A. Irvine, Oct 18 2018

References

• W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge, 1993, p. 158.

Programs

Maple

invA000292 := proc(n)
    local i;
    for i from 1 do
        if binomial(i+1,3) > n then
            return i;
        end if;
    end do:
end proc:
invA000217 := proc(n)
    local i;
    for i from 1 do
        if binomial(i+1,2) > n then
            return i;
        end if;
    end do:
end proc:
A014369 := proc(n)
    local b,c,d ;
    b := invA000292(n) ;
    c := invA000217(n-binomial(b,3)) ;
    d := n-binomial(b,3)-binomial(c,2) ;
    digcatL([b,c,d]) ; # of program transforms
end proc:
seq(A014369(n),n=1..70) ; # R. J. Mathar, May 25 2023

Extensions

a(1), a(4), a(10), a(20), a(35) modified to meet constraint b>c>d and more terms from Sean A. Irvine, Oct 18 2018