A134154 a(n) = 15*n^2 - 9*n + 1.

1, 7, 43, 109, 205, 331, 487, 673, 889, 1135, 1411, 1717, 2053, 2419, 2815, 3241, 3697, 4183, 4699, 5245, 5821, 6427, 7063, 7729, 8425, 9151, 9907, 10693, 11509, 12355, 13231, 14137, 15073, 16039, 17035, 18061, 19117, 20203, 21319, 22465, 23641

Offset: 0

Author

Artur Jasinski, Oct 10 2007

Keywords

• nonn
• easy

Comments

A119617 is union of A134153 and A134154 A000538(n) is divisible by A000330(n) if and only n is congruent to {1, 3} mod 5 (see A047219) A134154(n) is case when n is congruent to 3 mod 5 see cases 2)

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000538, A119617, A134153.

Programs

Mathematica

Table[1 - 9 n + 15 n^2, {n, 0, 50}]
Table[Sum[k^4, {k, 1, 5m + 3}]/Sum[k^2, {k, 1, 5m + 3}], {m, 0, 30}]

PARI

a(n)=15*n^2-9*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 15*n^2 - 9*n + 1.

a(n+1) = (3*(5*n + 3)^2 + 3*(5*n + 3) - 1)/5.

a(n+1) = (Sum_{k=1..5*n+3} k^4) / (Sum_{k=1..5*n+3} k^2).

G.f.: -(1+4*x+25*x^2)/(-1+x)^3. - R. J. Mathar, Nov 14 2007