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A070261 4th diagonal of triangle defined in A051537.

%I A070261 #11 Oct 08 2023 04:44:45
%S A070261 4,10,2,28,40,6,70,88,12,130,154,20,208,238,30,304,340,42,418,460,56,
%T A070261 550,598,72,700,754,90,868,928,110,1054,1120,132,1258,1330,156,1480,
%U A070261 1558,182,1720,1804,210,1978,2068,240,2254,2350,272,2548,2650,306,2860
%N A070261 4th diagonal of triangle defined in A051537.
%H A070261 Colin Barker, <a href="/A070261/b070261.txt">Table of n, a(n) for n = 1..1000</a>
%H A070261 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,1).
%F A070261 a(n) = lcm(n + 3, n) / gcd(n + 3, n).
%F A070261 From _Colin Barker_, Mar 27 2017: (Start)
%F A070261 G.f.: 2*x*(2 + 5*x + x^2 + 8*x^3 + 5*x^4 - x^6 - x^7) / ((1 - x)^3*(1 + x + x^2)^3).
%F A070261 a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>9.
%F A070261 (End)
%F A070261 From _Amiram Eldar_, Oct 08 2023: (Start)
%F A070261 Sum_{n>=1} 1/a(n) = 3/2.
%F A070261 Sum_{n>=1} (-1)^n/a(n) = 22*log(2)/9 - 7/6.
%F A070261 Sum_{k=1..n} a(k) ~ (19/81) * n^3. (End)
%t A070261 Table[ LCM[i + 3, i] / GCD[i + 3, i], {i, 1, 60}]
%o A070261 (PARI) Vec(2*x*(2 + 5*x + x^2 + 8*x^3 + 5*x^4 - x^6 - x^7) / ((1 - x)^3*(1 + x + x^2)^3) + O(x^60)) \\ _Colin Barker_, Mar 27 2017
%Y A070261 Cf. A051537.
%K A070261 nonn,easy
%O A070261 1,1
%A A070261 _Amarnath Murthy_, May 09 2002
%E A070261 Edited by _Robert G. Wilson v_, May 10 2002