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A070262 5th diagonal of triangle defined in A051537. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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]
Sequence in context: A369039 A049457 A061037 * A372289 A171621 A084183
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, May 09 2002
EXTENSIONS
Edited by Robert G. Wilson v, May 10 2002
STATUS
approved

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Last modified June 14 01:54 EDT 2024. Contains 373391 sequences. (Running on oeis4.)