A166925 Digital root of square of n-th triangular number.

1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9, 1, 9, 9

Offset: 1

Author

Zak Seidov, Oct 23 2009

Keywords

• base
• less
• easy
• nonn
• changed

Comments

Period is (1,9,9).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A000217, A000537, A010888.

Programs

Magma

&cat[[1,9,9]: n in [1..29]]; // Bruno Berselli, May 05 2011

Mathematica

Table[If[(m9 = Mod[(n(n + 1))^2/4, 9]) == 0, 9, m9], {n, 200}]

Formula

G.f.: x*(1+9*x+9*x^2)/(1-x^3). - Bruno Berselli, May 05 2011

a(n) = A010888(A000537(n)). - Michel Marcus, Mar 17 2023