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Sum of a square and a triangular number.
5

%I #13 Apr 28 2020 10:55:16

%S 0,1,2,3,4,5,6,7,9,10,11,12,14,15,16,17,19,21,22,24,25,26,28,29,30,31,

%T 32,35,36,37,39,40,42,44,45,46,49,50,51,52,53,54,55,56,57,59,61,64,65,

%U 66,67,70,71,72,74,75,77,78,79,80,81,82,84,85,87,91

%N Sum of a square and a triangular number.

%H Harvey P. Dale, <a href="/A014133/b014133.txt">Table of n, a(n) for n = 0..1000</a>

%F {k: A101428(k) > 0} .- _R. J. Mathar_, Apr 28 2020

%p isA014133 := proc(n)

%p local c,t ;

%p for c from 0 do

%p t := c*(c+1)/2 ;

%p if t > n then

%p return false;

%p end if;

%p if issqr(n-t) then

%p return true;

%p end if;

%p end do:

%p end proc:

%p for n from 0 to 100 do

%p if isA014133(n) then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Oct 11 2014

%t With[{nn=20},Select[Union[Flatten[Outer[Plus,Range[0,nn]^2,Accumulate[ Range[ 0,nn]]]]], #<=(nn(nn+1))/2&]] (* _Harvey P. Dale_, Dec 29 2019 *)

%Y Cf. A014134 (complement).

%K nonn

%O 0,3

%A _N. J. A. Sloane_.