A053220 a(n) = (3*n-1) * 2^(n-2).
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
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..500
- 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.
- Index entries for linear recurrences with constant coefficients, signature (4,-4).
Crossrefs
Programs
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Haskell
a053220 n = a056242 (n + 1) n -- Reinhard Zumkeller, May 08 2014
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Magma
[(3*n-1)*2^(n-2): n in [1..50]]; // Vincenzo Librandi, May 09 2011
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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 *) -
PARI
a(n)=if(n<1,0,(3*n-1)*2^(n-2))
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PARI
a(n)=(3*n-1)<<(n-2) \\ Charles R Greathouse IV, Apr 17 2012
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
Comments