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

1,1

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A051537.

Sequence in context: A337840 A349305 A244152 * A367029 A054048 A121512

Adjacent sequences: A070258 A070259 A070260 * A070262 A070263 A070264

Keyword

nonn,easy

Author

Amarnath Murthy, May 09 2002

Extensions

Edited by Robert G. Wilson v, May 10 2002

Status

approved