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A070260 Third diagonal of triangle defined in A051537. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, May 09 2002
EXTENSIONS
More terms from Vladeta Jovovic, May 09 2002
STATUS
approved

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Last modified June 18 11:45 EDT 2024. Contains 373481 sequences. (Running on oeis4.)