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

%I A073423 #35 Jan 19 2025 22:38:30
%S A073423 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,
%T A073423 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,
%U A073423 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
%N A073423 Sums of two powers of zero: triangle read by rows: T(m,n) = 0^n + 0^m, n >= 0, m = 0..n.
%H A073423 Antti Karttunen, <a href="/A073423/b073423.txt">Table of n, a(n) for n = 0..22154; the first 210 rows of the triangle</a>
%H A073423 Mohammad K. Azarian, <a href="https://doi.org/10.12988/imf.2022.912321">Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions</a>, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141.  See Conjecture 4.9, p. 138.
%F A073423 a(0) = 2; and for n > 0, a(n) = A010054(n). [As a flat sequence] - _Antti Karttunen_, Jan 19 2025
%e A073423 T(2,1) = 0^2 + 0^0 = 1.
%e A073423 Triangle begins:
%e A073423   2;
%e A073423   1, 0;
%e A073423   1, 0, 0;
%e A073423   1, 0, 0, 0;
%e A073423   1, 0, 0, 0, 0;
%e A073423   1, 0, 0, 0, 0, 0;
%e A073423   ...
%o A073423 (Python)
%o A073423 from math import isqrt
%o A073423 def A073423(n): return int((k:=n<<1)==(m:=isqrt(k))*(m+1)) if n else 2 # _Chai Wah Wu_, Nov 09 2024
%o A073423 (PARI) A073423(n) = if(!n,2,ispolygonal(n,3)); \\ _Antti Karttunen_, Jan 19 2025
%Y A073423 Cf. A023531, A010054, A073424.
%Y A073423 Column k=0 gives A054977.
%K A073423 easy,nonn,tabl
%O A073423 0,1
%A A073423 _Jeremy Gardiner_, Jul 30 2002