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A053220 a(n) = (3*n-1) * 2^(n-2). 20
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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..500

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).

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

Cf. A053219, A053221, A132776.

Center elements from triangle A053218. Also a diagonal of triangle A056242.

Sequence in context: A299810 A079094 A144952 * A048777 A300961 A270134

Adjacent sequences:  A053217 A053218 A053219 * A053221 A053222 A053223

KEYWORD

nonn,easy

AUTHOR

Asher Auel (asher.auel(AT)reed.edu), Jan 01 2000

STATUS

approved

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Last modified February 20 21:29 EST 2019. Contains 320350 sequences. (Running on oeis4.)