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A273373
Squares ending in digit 6.
5
16, 36, 196, 256, 576, 676, 1156, 1296, 1936, 2116, 2916, 3136, 4096, 4356, 5476, 5776, 7056, 7396, 8836, 9216, 10816, 11236, 12996, 13456, 15376, 15876, 17956, 18496, 20736, 21316, 23716, 24336, 26896, 27556, 30276, 30976, 33856, 34596, 37636, 38416, 41616
OFFSET
1,1
COMMENTS
These are the only squares whose second last digit is odd. This implies that the only squares whose last two digits are the same are those ending with 0 or 4; those ending with 1, 5, and 9 are paired with even second last digits. - Waldemar Puszkarz, May 24 2016
FORMULA
G.f.: 4*x*(4 + 5*x + 32*x^2 + 5*x^3 + 4*x^4)/((1 + x)^2*(1 - x)^3).
a(n) = 4*A047221(n)^2 = (10*n - 3*(-1)^n - 5)^2/4.
a(n) = A090773(n)^2. - Michel Marcus, May 25 2016
Sum_{n>=1} 1/a(n) = 2*Pi^2/(25*(5+sqrt(5))). - Amiram Eldar, Feb 16 2023
MAPLE
seq(seq((10*i+j)^2, j=[4, 6]), i=0..20); # Robert Israel, May 24 2016
MATHEMATICA
Table[(10 n - 3 (-1)^n - 5)^2/4, {n, 1, 50}]
CoefficientList[Series[4 (4 + 5 x + 32 x^2 + 5 x^3 + 4 x^4) / ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x]
Select[Range[250]^2, Mod[#, 10]==6&] (* Harvey P. Dale, May 31 2020 *)
PROG
(Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n, 2, 10) eq 6];
(Magma) [(10*n - 3*(-1)^n - 5)^2/4: n in [1..50]];
CROSSREFS
Cf. A017341 (numbers ending in 6), A017343 (cubes ending in 6).
Cf. squares with last digit k: A017270 (k=0), A273372 (k=1), A273375 (k=4), A017330 (k=5), this sequence (k=6), A273374 (k=9).
Sequence in context: A076956 A075369 A318425 * A264546 A218523 A300535
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, May 21 2016
EXTENSIONS
Corrected and extended by Bruno Berselli, May 23 2016
STATUS
approved