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%I #7 Jun 17 2017 04:36:49
%S 1,7,43,109,205,331,487,673,889,1135,1411,1717,2053,2419,2815,3241,
%T 3697,4183,4699,5245,5821,6427,7063,7729,8425,9151,9907,10693,11509,
%U 12355,13231,14137,15073,16039,17035,18061,19117,20203,21319,22465,23641
%N a(n) = 15n^2 - 9n + 1.
%C 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)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F 1) a(n) = 15n^2 - 9n + 1 2) a(n) = (3(5n + 3)^2 + 3 (5n + 3) - 1)/5 3) a(n) = sum[k^4]/sum[k^2], {k, 1, 5m + 3}]
%F G.f.: -(1+4*x+25*x^2)/(-1+x)^3. - _R. J. Mathar_, Nov 14 2007
%t 1) Table[1 - 9 n + 15 n^2, {n, 0, 50}] 2) Table[Sum[k^4, {k, 1, 5m + 3}]/Sum[k^2, {k, 1, 5m + 3}], {m, 0, 30}] (*Artur Jasinski*)
%o (PARI) a(n)=15*n^2-9*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000538, A119617, A134153.
%K nonn,easy
%O 0,2
%A _Artur Jasinski_, Oct 10 2007
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