A070262 5th diagonal of triangle defined in A051537.

5, 3, 21, 2, 45, 15, 77, 6, 117, 35, 165, 12, 221, 63, 285, 20, 357, 99, 437, 30, 525, 143, 621, 42, 725, 195, 837, 56, 957, 255, 1085, 72, 1221, 323, 1365, 90, 1517, 399, 1677, 110, 1845, 483, 2021, 132, 2205, 575, 2397, 156, 2597, 675, 2805, 182, 3021, 783

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

Formula

a(n) = lcm(n + 4, n) / gcd(n + 4, n).

From Colin Barker, Mar 27 2017: (Start)

G.f.: x*(5 + 3*x + 21*x^2 + 2*x^3 + 30*x^4 + 6*x^5 + 14*x^6 - 3*x^8 - x^9 - 3*x^10) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3).

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) for n>12. (End)

From Luce ETIENNE, May 10 2018: (Start)

a(n) = n*(n+4)*4^((5*(n mod 4)^3 - 24*(n mod 4)^2 + 31*(n mod 4)-12)/6).

a(n) = n*(n+4)*(37-27*cos(n*Pi)-6*cos(n*Pi/2))/64. (End)

From Amiram Eldar, Oct 08 2023: (Start)

Sum_{n>=1} 1/a(n) = 11/6.

Sum_{n>=1} (-1)^n/a(n) = 7/6.

Sum_{k=1..n} a(k) ~ (37/192) * n^3. (End)

Mathematica

Table[ LCM[i + 4, i] / GCD[i + 4, i], {i, 1, 60}]
LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {5, 3, 21, 2, 45, 15, 77, 6, 117, 35, 165, 12}, 90] (* Harvey P. Dale, Jul 13 2019 *)

Prog

(PARI) Vec(x*(5 + 3*x + 21*x^2 + 2*x^3 + 30*x^4 + 6*x^5 + 14*x^6 - 3*x^8 - x^9 - 3*x^10) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3) + O(x^60)) \\ Colin Barker, Mar 27 2017
(PARI) a(n) = lcm(n+4, n)/gcd(n+4, n); \\ Altug Alkan, Sep 20 2018
(Magma) [LCM(n + 4, n)/GCD(n + 4, n): n in [1..50]]; // G. C. Greubel, Sep 20 2018

Crossrefs

Cf. A061037. [From R. J. Mathar, Sep 29 2008]

Cf. A010873, A051537.

Cf. A000466, A002378, A003185, A085027.

Sequence in context: A369039 A049457 A061037 * A171621 A084183 A099730

Adjacent sequences: A070259 A070260 A070261 * A070263 A070264 A070265

Keyword

nonn,easy

Author

Amarnath Murthy, May 09 2002

Extensions

Edited by Robert G. Wilson v, May 10 2002

Status

approved