A255680 a(n) = n*(n mod 3)*(n mod 5).

0, 1, 8, 0, 16, 0, 0, 14, 48, 0, 0, 22, 0, 39, 112, 0, 16, 68, 0, 76, 0, 0, 44, 138, 0, 0, 52, 0, 84, 232, 0, 31, 128, 0, 136, 0, 0, 74, 228, 0, 0, 82, 0, 129, 352, 0, 46, 188, 0, 196, 0, 0, 104, 318, 0, 0, 112, 0, 174, 472, 0, 61, 248, 0, 256, 0, 0, 134, 408, 0, 0, 142, 0, 219, 592, 0, 76, 308, 0, 316, 0, 0, 164, 498, 0, 0, 172, 0

Offset: 0

Author

Zak Seidov, Mar 01 2015

Keywords

• nonn
• easy

Comments

a(n) = 0 for n = 3k and 5k, k=0,1,2,...

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, -1).

Crossrefs

Cf. A255642.

Programs

Magma

[n*(n mod 3)*(n mod 5): n in [0..80]]; // Vincenzo Librandi, Mar 03 2015

Mathematica

Table[x*Mod[x, 3]*Mod[x, 5], {x, 0, 100}]
LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1},{0,1,8,0,16,0,0,14,48,0,0,22,0,39,112,0,16,68,0,76,0,0,44,138,0,0,52,0,84,232},100] (* Harvey P. Dale, Sep 06 2015 *)

PARI

vector(101, n, (n-1)*((n-1)%3)*((n-1)%5))

Formula

Empirical g.f.: x*(8*x^28 + 6*x^27 + 8*x^25 + 42*x^22 + 16*x^21 + 44*x^18 + 52*x^16 + 14*x^15 + 112*x^13 + 39*x^12 + 22*x^10 + 48*x^7 + 14*x^6 + 16*x^3 + 8*x + 1) / ((x - 1)^2*(x^2 + x + 1)^2*(x^4 + x^3 + x^2 + x + 1)^2*(x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)^2). - Colin Barker, Mar 02 2015

a(n) = n*A010872(n)*A010874(n). - Michel Marcus, Mar 03 2015

Extensions

Typo in first Mathematica program corrected by Harvey P. Dale, Jul 03 2021