A134153 - OEIS

A134153

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

1, 25, 79, 163, 277, 421, 595, 799, 1033, 1297, 1591, 1915, 2269, 2653, 3067, 3511, 3985, 4489, 5023, 5587, 6181, 6805, 7459, 8143, 8857, 9601, 10375, 11179, 12013, 12877, 13771, 14695, 15649, 16633, 17647, 18691, 19765, 20869, 22003, 23167

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OFFSET

0,2

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 1 mod 5 see cases 2)

LINKS

Table of n, a(n) for n=0..39.

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

FORMULA

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

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

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

G.f.: -(1+22*x+7*x^2)/(-1+x)^3. - R. J. Mathar, Nov 14 2007

MATHEMATICA

Table[1 + 9 n + 15 n^2, {n, 0, 50}]

Table[Sum[k^4, {k, 1, 5m + 1}]/Sum[k^2, {k, 1, 5m + 1}], {m, 0, 10}]

PROG