A273375 Squares ending in digit 4.

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

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

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. A000290, A047209.

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

Adjacent sequences: A273372 A273373 A273374 * A273376 A273377 A273378

Keyword

nonn,base,easy

Author

Vincenzo Librandi, May 24 2016

Extensions

Edited by Bruno Berselli, May 24 2016

Status

approved