A070261 4th diagonal of triangle defined in A051537.

4, 10, 2, 28, 40, 6, 70, 88, 12, 130, 154, 20, 208, 238, 30, 304, 340, 42, 418, 460, 56, 550, 598, 72, 700, 754, 90, 868, 928, 110, 1054, 1120, 132, 1258, 1330, 156, 1480, 1558, 182, 1720, 1804, 210, 1978, 2068, 240, 2254, 2350, 272, 2548, 2650, 306, 2860

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 (0,0,3,0,0,-3,0,0,1).

Crossrefs

Cf. A051537.

Programs

Mathematica

Table[ LCM[i + 3, i] / GCD[i + 3, i], {i, 1, 60}]

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

Formula

a(n) = lcm(n + 3, n) / gcd(n + 3, n).

From Colin Barker, Mar 27 2017: (Start)

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).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>9.

(End)

From Amiram Eldar, Oct 08 2023: (Start)

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

Sum_{n>=1} (-1)^n/a(n) = 22*log(2)/9 - 7/6.

Sum_{k=1..n} a(k) ~ (19/81) * n^3. (End)

Extensions

Edited by Robert G. Wilson v, May 10 2002