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A053220 a(n) = (3*n-1) * 2^(n-2). 25
1, 5, 16, 44, 112, 272, 640, 1472, 3328, 7424, 16384, 35840, 77824, 167936, 360448, 770048, 1638400, 3473408, 7340032, 15466496, 32505856, 68157440, 142606336, 297795584, 620756992, 1291845632, 2684354560, 5570035712, 11542724608, 23890755584, 49392123904 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Coefficients in the hypergeometric series identity 1 - 5*x/(x + 4) + 16*x*(x - 1)/((x + 4)*(x + 6)) - 44*x*(x - 1)*(x - 2)/((x + 4)*(x + 6)*(x + 8)) + ... = 0, valid in the half-plane Re(x) > 0. Cf. A276289. - Peter Bala, May 30 2019
LINKS
Marcella Anselmo, Giuseppa Castiglione, Manuela Flores, Dora Giammarresi, Maria Madonia, and Sabrina Mantaci, Hypercubes and Isometric Words based on Swap and Mismatch Distance, arXiv:2303.09898 [math.CO], 2023.
F. K. Hwang and C. L. Mallows, Enumerating nested and consecutive partitions, J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333.
FORMULA
G.f.: x*(1+x)/(1-2*x)^2.
a(n) = (3*n-1) * 2^(n-2).
E.g.f.: exp(2*x)*(1+3*x). The sequence 0, 1, 5, 16, ... has a(n) = ((3n-1)*2^n + 0^n)/4 (offset 0). It is the binomial transform of A032766. The sequence 1, 5, 16, ... has a(n) = (2+3n)*2^(n-1) (offset 0). It is the binomial transform of A016777. - Paul Barry, Jul 23 2003
Row sums of A132776(n-1). - Gary W. Adamson, Aug 29 2007
a(n+1) = det(f(i-j+1))_{1 <= i, j <= n}, where f(0) = 1, f(1) = 5 and for k > 0, we have f(k+1) = 9 and f(-k) = 0. - Mircea Merca, Jun 23 2012
MATHEMATICA
ListCorrelate[{1, 1}, Table[n 2^(n - 1), {n, 0, 28}]] (* or *) ListConvolve[{1, 1}, Table[n 2^(n - 1), {n, 0, 28}]] (* Ross La Haye, Feb 24 2007 *)
LinearRecurrence[{4, -4}, {1, 5}, 35] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
Array[(3# - 1) 2^(# - 2) &, 35] (* Alonso del Arte, Sep 04 2018 *)
CoefficientList[Series[(1 + x)/(1 - 2 * x)^2, {x, 0, 50}], x] (* Stefano Spezia, Sep 04 2018 *)
PROG
(PARI) a(n)=if(n<1, 0, (3*n-1)*2^(n-2))
(PARI) a(n)=(3*n-1)<<(n-2) \\ Charles R Greathouse IV, Apr 17 2012
(Magma) [(3*n-1)*2^(n-2): n in [1..50]]; // Vincenzo Librandi, May 09 2011
(Haskell)
a053220 n = a056242 (n + 1) n -- Reinhard Zumkeller, May 08 2014
CROSSREFS
Center elements from triangle A053218. Also a diagonal of triangle A056242.
Sequence in context: A299810 A079094 A144952 * A048777 A300961 A270134
KEYWORD
nonn,easy
AUTHOR
Asher Auel, Jan 01 2000
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)