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 A372718 Triangular numbers that are 2 mod 4, halved. 0
 3, 5, 33, 39, 95, 105, 189, 203, 315, 333, 473, 495, 663, 689, 885, 915, 1139, 1173, 1425, 1463, 1743, 1785, 2093, 2139, 2475, 2525, 2889, 2943, 3335, 3393, 3813, 3875, 4323, 4389, 4865, 4935, 5439, 5513, 6045, 6123, 6683, 6765, 7353, 7439, 8055, 8145, 8789, 8883, 9555, 9653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sum of the first 2*a(n) numbers of any Fibonacci-like sequence equals its (a(n)+2)-nd term times the a(n)-th Lucas number. LINKS Table of n, a(n) for n=1..50. Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = A000217(A047457(n))/2 = A372070(n)/2. EXAMPLE 10 is a triangular number that has a remainder of 2 when divided by 4. Therefore, its half, 5, is in this sequence. Moreover, the sum of the first 5*2 Fibonacci numbers is 143 (not counting zero). This sum is a product of 13, which is the (5+2 = 7)-th term of the Fibonacci sequence times 11, which is the fifth Lucas number. MATHEMATICA Select[Table[n (n + 1)/2, {n, 200}], Mod[#, 4] == 2 &]/2 CROSSREFS Cf. A000032, A000045, A000217. A372048, A372049, A372050, A372051, A372070. Sequence in context: A199774 A235267 A284379 * A103010 A225866 A332704 Adjacent sequences: A372715 A372716 A372717 * A372719 A372720 A372721 KEYWORD nonn,easy AUTHOR Tanya Khovanova and the PRIMES STEP senior group, May 11 2024 STATUS approved

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Last modified August 2 19:53 EDT 2024. Contains 374875 sequences. (Running on oeis4.)