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A166539 a(n) = (10*n + 7*(-1)^n + 5)/4. 1
2, 8, 7, 13, 12, 18, 17, 23, 22, 28, 27, 33, 32, 38, 37, 43, 42, 48, 47, 53, 52, 58, 57, 63, 62, 68, 67, 73, 72, 78, 77, 83, 82, 88, 87, 93, 92, 98, 97, 103, 102, 108, 107, 113, 112, 118, 117, 123, 122, 128, 127, 133, 132, 138, 137, 143, 142, 148, 147, 153, 152, 158 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = 5*n - a(n-1), n>=2.
From Harvey P. Dale, Jun 29 2011: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3), n>=4.
G.f.: x*(2-3*x*(x-2))/((x-1)^2*(x+1)). (End)
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (1/4)*(5*(1 + 2*x)*exp(x) + 7*exp(-x) - 12).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/3 + sqrt((5-2*sqrt(5))/5)*Pi/5. - Amiram Eldar, Feb 24 2023
EXAMPLE
For n=2, a(2)=5*2-2=8; n=3, a(3)=5*3-8=7; n=4, a(4)=5*4-7=13.
MATHEMATICA
RecurrenceTable[{a[1]==2, a[n]==5n-a[n-1]}, a[n], {n, 70}] (* or *) LinearRecurrence[{1, 1, -1}, {2, 8, 7}, 70] (* Harvey P. Dale, Jun 29 2011 *)
PROG
(Magma) [5*n/2 + (5+7*(-1)^n)/4: n in [1..70]]; // Vincenzo Librandi, May 15 2013
CROSSREFS
Sequence in context: A079031 A203145 A303498 * A344718 A075429 A344692
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 16 2009
STATUS
approved

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Last modified June 18 11:09 EDT 2024. Contains 373481 sequences. (Running on oeis4.)