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 A328791 Triangular numbers of the form k^2 + 3. 1
 3, 28, 903, 30628, 1040403, 35343028, 1200622503, 40785822028, 1385517326403, 47066803275628, 1598885794044903, 54315050194251028, 1845112820810490003, 62679520857362409028, 2129258596329511416903, 72332112754346025765628, 2457162575051435364614403 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). LINKS FORMULA a(1) = 3, a(2) = 28; for n > 2, a(n) = 34*a(n-1) - a(n-2) - 46. PROG (Python) limit = 10**7 # rough limit for k A000217 = set(k*(k+1)//2 for k in range(14*limit//10)) A117950 = set(k**2 + 3 for k in range(limit)) print(sorted(A000217 & A117950)) # Michael S. Branicky, Mar 28 2021 CROSSREFS Cf. A001110, A164055, A214838, A328792. Intersection of A000217 and A117950. Sequence in context: A015474 A324462 A053601 * A140990 A196735 A208438 Adjacent sequences:  A328788 A328789 A328790 * A328792 A328793 A328794 KEYWORD nonn AUTHOR Jon E. Schoenfield, Oct 27 2019 STATUS approved

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Last modified May 17 18:44 EDT 2021. Contains 343987 sequences. (Running on oeis4.)