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
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
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
KEYWORD
nonn,easy
AUTHOR
Tanya Khovanova and the PRIMES STEP senior group, May 11 2024
STATUS
approved