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

1,1

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).

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)

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 *)

Prog

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

Crossrefs

Bisections: A002378, A000466.

Cf. A051537.

Sequence in context: A086485 A068310 A033314 * A142705 A072346 A334865

Adjacent sequences: A070257 A070258 A070259 * A070261 A070262 A070263

Keyword

nonn,easy

Author

Amarnath Murthy, May 09 2002

Extensions

More terms from Vladeta Jovovic, May 09 2002

Status

approved