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a(0)=3. a(n) = number of earlier terms which, each added to n, sum to a square.
1

%I #7 Jun 13 2016 08:33:45

%S 3,1,0,1,1,0,1,0,4,3,0,0,1,2,1,6,5,0,0,1,1,1,2,2,9,7,0,1,0,1,1,1,1,2,

%T 4,14,9,0,0,0,2,0,1,1,1,2,2,7,17,13,1,1,0,0,0,2,0,2,1,1,2,2,11,21,18,

%U 0,0,1,1,0,1,0,2,0,2,1,1,2,2,16,26,22,1,1

%N a(0)=3. a(n) = number of earlier terms which, each added to n, sum to a square.

%C Does every nonnegative integer occur eventually? Analogous to A123396 a(0)=0. a(n) = number of earlier terms each of which, when added to n, the sum is a triangular number.

%H Giovanni Resta, <a href="/A121383/b121383.txt">Table of n, a(n) for n = 0..1000</a>

%e a(6) = 1 because the previous terms are 3, 1, 0, 1, 1, 0, and among them only one (3) added to 6 gives a square (9).

%t a[0] = 3; a[n_] := a[n] = Length@ Select[ Range[0, n-1], IntegerQ@ Sqrt[n + a[#]] &]; a /@ Range[0, 90] (* _Giovanni Resta_, Jun 13 2016 *)

%Y Cf. A123396.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Oct 14 2006

%E Data section corrected and extended by _Giovanni Resta_, Jun 13 2016