A328791 - OEIS

%I #12 Sep 15 2021 11:15:57

%S 3,28,903,30628,1040403,35343028,1200622503,40785822028,1385517326403,

%T 47066803275628,1598885794044903,54315050194251028,

%U 1845112820810490003,62679520857362409028,2129258596329511416903,72332112754346025765628,2457162575051435364614403

%N Triangular numbers of the form k^2 + 3.

%C There exist triangular numbers of the form k^2 + j for j=0 (A001110), j=1 (A164055), j=2 (A214838), and j=3 (this sequence), but not for j=4,7,8,13,16,18,... (A328792).

%F a(1) = 3, a(2) = 28; for n > 2, a(n) = 34*a(n-1) - a(n-2) - 46.

%o (Python)

%o limit = 10**7 # rough limit for k

%o A000217 = set(k*(k+1)//2 for k in range(14*limit//10))

%o A117950 = set(k**2 + 3 for k in range(limit))

%o print(sorted(A000217 & A117950)) # _Michael S. Branicky_, Mar 28 2021

%Y Cf. A001110, A164055, A214838, A328792.

%Y Intersection of A000217 and A117950.

%Y Cf. A276598 (the k's).

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Oct 27 2019