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A345376 Number of Companion Pell numbers m <= n. 1
0, 0, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Table 1 of Andrica 2021 paper (p. 24) refers to A002203 as "Pell-Lucas" numbers.
LINKS
Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, On some new results for the generalised Lucas sequences, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36. See Section 5.2, pp. 32-33, Table 3.
EXAMPLE
The Pell-Lucas numbers A002203 are 2, 2, 6, 14, 34, 82, ...
a(0)=a(1)=0, since there are no Pell-Lucas numbers less than or equal to 0 and 1, respectively.
a(2)=a(3)=a(4)=a(5)=2, since the first 2 Pell-Lucas numbers, 2 and 2, are less than or equal to 2, 3, 4, and 5, respectively.
MATHEMATICA
Block[{a = 2, b = -1, nn = 64, u, v = {}}, u = {2, a}; Do[AppendTo[u, Total[{-b, a} u[[-2 ;; -1]]]]; AppendTo[v, Count[u, _?(# <= i &)]], {i, nn}]; {Boole[First[u] <= 0]}~Join~v] (* Michael De Vlieger, Jun 16 2021 *)
CROSSREFS
Cf. A002203, A108852 (Fibonacci), A130245 (Lucas), A335741 (Pell).
Sequence in context: A235037 A347966 A186437 * A029835 A074280 A000523
KEYWORD
nonn,easy
AUTHOR
Ovidiu Bagdasar, Jun 16 2021
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)