A378170 Number of subsets of the first n nonzero tetrahedral numbers whose sum is a nonzero tetrahedral number.

1, 2, 3, 5, 7, 8, 11, 13, 19, 34, 45, 72, 113, 171, 262, 388, 638, 1128, 1928, 3370, 5584, 9691, 17129, 30493, 54785, 94510, 169817, 308491, 559176, 1019487, 1816043, 3333698, 6153695, 11384025, 21100254, 38262081, 71096456, 132675454, 247900732, 463959984

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..103

Example

a(8) = 13 subsets: {1}, {4}, {10}, {20}, {35}, {56}, {84}, {120}, {1, 20, 35}, {1, 35, 84}, {10, 35, 120}, {1, 4, 10, 20} and {1, 4, 20, 56, 84}.

Prog

(Python)
from sympy import integer_nthroot
def is_tetra(n): return (c:=integer_nthroot(6*n, 3)[0])*(c+1)*(c+2) == 6*n
from functools import cache
@cache
def b(n, s):
    if n == 0:
        if s > 0 and is_tetra(s): return 1
        return 0
    return b(n-1, s) + b(n-1, s+n*(n+1)*(n+2)//6)
a = lambda n: b(n, 0)
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Nov 18 2024

Crossrefs

Cf. A000292, A377123, A378171.

Sequence in context: A174895 A375270 A186285 * A375886 A190855 A190810

Adjacent sequences: A378161 A378162 A378168 * A378171 A378173 A378174

Keyword

nonn,new

Author

Ilya Gutkovskiy, Nov 18 2024

Extensions

a(24) and beyond from Michael S. Branicky, Nov 18 2024

Status

approved