A070260 Third diagonal of triangle defined in A051537.

3, 2, 15, 6, 35, 12, 63, 20, 99, 30, 143, 42, 195, 56, 255, 72, 323, 90, 399, 110, 483, 132, 575, 156, 675, 182, 783, 210, 899, 240, 1023, 272, 1155, 306, 1295, 342, 1443, 380, 1599, 420, 1763, 462, 1935, 506, 2115, 552, 2303, 600, 2499, 650, 2703, 702

Offset: 1

Author

Amarnath Murthy, May 09 2002

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Bisections: A002378, A000466.

Cf. A051537.

Programs

Mathematica

Table[ LCM[i + 2, i] / GCD[i + 2, i], {i, 1, 60}]
LinearRecurrence[{0,3,0,-3,0,1},{3,2,15,6,35,12},60] (* Harvey P. Dale, Sep 14 2019 *)

PARI

Vec(x*(3+2*x+6*x^2-x^4) / (1-x^2)^3 + O(x^60)) \\ Colin Barker, Mar 27 2017

Formula

From Vladeta Jovovic, May 09 2002: (Start)

a(n) = n*(n+2)/4 if n is even else n*(n+2).

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).

G.f.: x*(3 + 2*x + 6*x^2 - x^4)/(1 - x^2)^3. (End)

E.g.f.: (x/4)*((12 + x)*cosh(x) + (3 + 4*x)*sinh(x)). - G. C. Greubel, Jul 20 2017

From Amiram Eldar, Oct 08 2023: (Start)

Sum_{n>=1} 1/a(n) = 3/2.

Sum_{n>=1} (-1)^n/a(n) = 1/2.

Sum_{k=1..n} a(k) ~ (5/24) * n^3. (End)

Extensions

More terms from Vladeta Jovovic, May 09 2002