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A086972 a(n) = n*3^(n-1) + (3^n + 1)/2. 3
1, 3, 11, 41, 149, 527, 1823, 6197, 20777, 68891, 226355, 738113, 2391485, 7705895, 24712007, 78918989, 251105873, 796364339, 2518233179, 7942120025, 24988621541, 78452649023, 245818300271, 768835960421, 2400651060089 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Binomial transform of A057711 (without leading zero). Second binomial transform of (1,1,3,3,5,5,7,7,9,9,11,11,...).
LINKS
FORMULA
a(n) = (1/2)*(A081038(n) + 1).
G.f.: (1-4*x+5*x^2)/((1-x)*(1-3*x)^2).
a(n) = A027471(n) + A007051(n).
E.g.f.: (1/2)*( exp(x) + (2*x+1)*exp(3*x) ). - G. C. Greubel, Nov 24 2023
MATHEMATICA
Table[((2*n+3)*3^(n-1) +1)/2, {n, 0, 30}] (* G. C. Greubel, Nov 24 2023 *)
PROG
(Magma) [n*3^(n-1) + (3^n+1)/2: n in [0..30]]; // Vincenzo Librandi, Jun 09 2011
(PARI) Vec((1-4*x+5*x^2)/((1-x)*(1-3*x)^2) + O(x^40)) \\ Michel Marcus, Mar 08 2016
(SageMath) [((2*n+3)*3^(n-1) +1)//2 for n in range(31)] # G. C. Greubel, Nov 24 2023
CROSSREFS
Partial sums of A199923.
Sequence in context: A075276 A242233 A294504 * A218348 A320827 A335793
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 26 2003
STATUS
approved

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Last modified June 12 18:11 EDT 2024. Contains 373359 sequences. (Running on oeis4.)