OFFSET
1,2
COMMENTS
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.: x*(1 + 80*x + 38*x^2 + 80*x^3 + x^4) / ((1 + x)^2*(1 - x)^3).
a(n) = 10*A132356(n-1) + 1 = 5*(10*n+(-1)^n-5)*(2*n+(-1)^n-1)/4+1.
a(n) = (5*n - 5/2 + (3/2)*(-1)^n)^2 = 25*n^2 - 25*n + 17/2 + 15*n*(-1)^n - (15/2)*(-1)^n. - David A. Corneth, May 21 2016
a(n) = A090771(n)^2. - Michel Marcus, May 25 2016
Sum_{n>=1} 1/a(n) = Pi^2*(3+sqrt(5))/50. - Amiram Eldar, Feb 16 2023
MATHEMATICA
Table[5 (10 n + (-1)^n - 5) (2 n + (-1)^n - 1)/4 + 1, {n, 1, 50}]
PROG
(Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n, 2, 10) eq 1];
(Magma) [5*(10*n+(-1)^n-5)*(2*n+(-1)^n-1)/4+1: n in [1..50]];
(Ruby) p (1..(n + 1) / 2).inject([]){|s, i| s + [(10 * i - 9) ** 2, (10 * i - 1) ** 2]}[0..n - 1] # Seiichi Manyama, May 24 2016
(Python)
A273372_list = [(10*n+m)**2 for n in range(10**3) for m in (1, 9)] # Chai Wah Wu, May 24 2016
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Vincenzo Librandi, May 21 2016
EXTENSIONS
Edited by Bruno Berselli, May 24 2016
STATUS
approved