[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A085281
Expansion of (1 - 3*x + x^2)/((1-2*x)*(1-3*x)).
3
1, 2, 5, 13, 35, 97, 275, 793, 2315, 6817, 20195, 60073, 179195, 535537, 1602515, 4799353, 14381675, 43112257, 129271235, 387682633, 1162785755, 3487832977, 10462450355, 31385253913, 94151567435, 282446313697, 847322163875, 2541932937193, 7625731702715, 22877060890417, 68630914235795, 205892205836473
OFFSET
0,2
COMMENTS
Binomial transform of A005578.
Binomial transform is A085282.
FORMULA
a(n) = 3^(n-1) + 2^(n-1) + 0^n/6.
a(n) = A007689(n-1), n > 0. - R. J. Mathar, Sep 12 2008
E.g.f.: (1/6)*(1 + 3*exp(2*x) + 2*exp(3*x)). - G. C. Greubel, Nov 11 2024
MATHEMATICA
a[n_]:=3^n/3 + 2^n/2; Flatten[Join[{1, Array[a, 50]}]] (* or *)
CoefficientList[Series[(1 - 3*x + x^2)/((1-2*x)*(1-3*x)), {x, 0, 50}], x] (* Stefano Spezia, Sep 09 2018 *)
LinearRecurrence[{5, -6}, {1, 2, 5}, 40] (* Harvey P. Dale, Jun 14 2022 *)
PROG
(Magma) [3^n/3+2^n/2+0^n/6: n in [0..40]]; // Vincenzo Librandi, May 29 2011
(SageMath)
def A085281(n): return 2^(n-1) +3^(n-1) +int(n==0)/6
[A085281(n) for n in range(41)] # G. C. Greubel, Nov 11 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 25 2003
STATUS
approved