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A053220
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(3n-1)2^(n-2), n>0.
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16
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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; internal format)
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OFFSET
| 1,2
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REFERENCES
| Hwang, F. K.; Mallows, C. L.; Enumerating nested and consecutive partitions. J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..500
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FORMULA
| G.f.: x(1+x)/(1-2x)^2. a(n)=(3n-1)2^(n-2).
E.g.f. exp(2x)(1+3x). 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 (pbarry(AT)wit.ie), Jul 23 2003
Row sums of A132776(n-1). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2007
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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 (rlahaye(AT)new.rr.com), Feb 24 2007
LinearRecurrence[{4, -4}, {1, 5}, 35] (* From Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
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PROG
| (PARI) a(n)=if(n<1, 0, (3*n-1)*2^(n-2))
(MAGMA) [(3*n-1)*2^(n-2): n in [1..30]]; // Vincenzo Librandi, May 09 2011
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CROSSREFS
| Cf. A053218, A053219, A053221.
Center elements from triangle A053218. Also a diagonal of triangle A056242.
Cf. A132776.
Sequence in context: A137234 A079094 A144952 * A048777 A185003 A189390
Adjacent sequences: A053217 A053218 A053219 * A053221 A053222 A053223
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KEYWORD
| nonn
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AUTHOR
| Asher Auel (asher.auel(AT)reed.edu), Jan 01 2000
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