A073423 Sums of two powers of zero: triangle read by rows: T(m,n) = 0^n + 0^m, n >= 0, m = 0..n.

2, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Jeremy Gardiner, Jul 30 2002

Keywords

• easy
• nonn
• tabl

Examples

			T(2,1) = 0^2 + 0^0 = 1.
Triangle begins:
  2;
  1, 0;
  1, 0, 0;
  1, 0, 0, 0;
  1, 0, 0, 0, 0;
  1, 0, 0, 0, 0, 0;
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..22154; the first 210 rows of the triangle
• Mohammad K. Azarian, Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141. See Conjecture 4.9, p. 138.

Crossrefs

Cf. A023531, A010054, A073424.

Column k=0 gives A054977.

Programs

PARI

A073423(n) = if(!n,2,ispolygonal(n,3)); \\ Antti Karttunen, Jan 19 2025

Python

from math import isqrt
def A073423(n): return int((k:=n<<1)==(m:=isqrt(k))*(m+1)) if n else 2 # Chai Wah Wu, Nov 09 2024

Formula

a(0) = 2; and for n > 0, a(n) = A010054(n). [As a flat sequence] - Antti Karttunen, Jan 19 2025