A056559 Tetrahedron with T(t,n,k) = t - n; succession of growing finite triangles with declining values per row.

0, 1, 0, 0, 2, 1, 1, 0, 0, 0, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2

Offset: 0

Author

Henry Bottomley, Jun 26 2000

Keywords

• nonn
• look

Examples

			First triangle: [0]; second triangle: [1; 0 0]; third triangle: [2; 1 1; 0 0 0]; ...
		

Links

• Peter Luschny, Table of n, a(n) for n = 0..10000 (first 105 terms by Henry Bottomley).

Crossrefs

Together with A056558 and A056560 might enable reading "by antidiagonals" of cube arrays as 3-dimensional analog of A002262 and A025581 with square arrays.

Bisection (y-coordinates) of A332662.

Programs

Julia

function a_list(N)
    a = Int[]
    for n in 1:N
        for j in ((k:-1:1) for k in 1:n)
            t = n - j[1]
            for m in j
                push!(a, t)
end end end; a end
A = a_list(10) # Peter Luschny, Feb 19 2020

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A056559(n): return (m:=integer_nthroot(6*(n+1),3)[0])-(a:=nChai Wah Wu, Dec 11 2024

Formula

a(n) = A056556(n) - A056557(n).