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A273375 Squares ending in digit 4. 5
4, 64, 144, 324, 484, 784, 1024, 1444, 1764, 2304, 2704, 3364, 3844, 4624, 5184, 6084, 6724, 7744, 8464, 9604, 10404, 11664, 12544, 13924, 14884, 16384, 17424, 19044, 20164, 21904, 23104, 24964, 26244, 28224, 29584, 31684, 33124, 35344, 36864, 39204 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
G.f.: 4*x*(1 + 15*x + 18*x^2 + 15*x^3 + x^4) /((1+x)^2*(1-x)^3).
a(n) = 4*A047209(n)^2 = (10*n + (-1)^n - 5)^2/4.
Sum_{n>=1} 1/a(n) = 2*Pi^2/(25*(5-sqrt(5))). - Amiram Eldar, Feb 16 2023
MATHEMATICA
Table[(10 n + (-1)^n - 5)^2/4, {n, 1, 50}] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {4, 64, 144, 324, 484}, 50]
Select[Range[200]^2, Mod[#, 10]==4&] (* or *) LinearRecurrence[{1, 1, -1}, {2, 8, 12}, 40]^2(* Harvey P. Dale, Aug 06 2017 *)
PROG
(Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n, 2, 10) eq 4];
(Magma) [(10*n+(-1)^n-5)^2/4: n in [1..50]];
CROSSREFS
Cf. A017317 (numbers ending in 4), A017319 (cubes ending in 4).
Cf. similar sequences listed in A273373.
Sequence in context: A210935 A090561 A364453 * A016934 A260182 A056229
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, May 24 2016
EXTENSIONS
Edited by Bruno Berselli, May 24 2016
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)