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
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*(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
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, May 21 2016
EXTENSIONS
Corrected and extended by Bruno Berselli, May 23 2016
STATUS
approved