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A145563
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a(0)=0 and a(n+1)=3*a(n)+2^(n+2).
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2
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0, 4, 20, 76, 260, 844, 2660, 8236, 25220, 76684, 232100, 700396, 2109380, 6344524, 19066340, 57264556, 171924740, 516036364, 1548633380, 4646948716, 13942943300, 41833024204, 125507461220, 376539160876, 1129651037060, 3389020220044, 10167194877860
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Suggested by a discussion on the Sequence Fans Mailing List; the formula is due to Andrew V. Sutherland.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..170
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FORMULA
| a(n)=4*(3^n-2^n)=4*A001047(n). G.f.: 4*x/((1-2*x)*(1-3*x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 18 2009]
a(n) = 4*(3^n - 2^n) = A056182(n)*2. [From Omar E. Pol (info(AT)polprimos.com), Mar 18 2009]
a(n) = A001047(n)*4. [From Omar E. Pol (info(AT)polprimos.com), Mar 18 2009]
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MATHEMATICA
| CoefficientList[Series[4x/((1-2x)(1-3x)), {x, 0, 40}], x] (* or *) RecurrenceTable[{a[0]==0 , a[n]==(3a[n-1]+2^(n+1))}, a, {n, 40}] (* From Harvey P. Dale, Apr 24 2011 *)
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PROG
| (MAGMA) [ 4*(3^n - 2^n): n in [0..50]]; // Vincenzo Librandi, Apr 24 2011
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CROSSREFS
| Cf. A056182, A001047. [From Omar E. Pol (info(AT)polprimos.com), Mar 18 2009]
Sequence in context: A196432 A196508 A121257 * A125669 A082138 A074358
Adjacent sequences: A145560 A145561 A145562 * A145564 A145565 A145566
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 18 2009
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