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A084215
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G.f.: (1+x^2)/(1-2x).
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6
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1, 2, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120, 10737418240
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Associated with a math magic problem.
Elements are the sums of consecutive pairs of elements of A084214.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n)=sum(k=0..n, 2^(n-k)*binomial(1, k/2)*(1+(-1)^k)/2 ) - Paul Barry (pbarry(AT)wit.ie), Oct 15 2004
a(n)=A020714(n-2), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 19 2008]
a(n) is the sum of top row terms of M^n, M = an infinite square production matrix as follows:
1, 1, 0, 0, 0, 0,...
1, 1, 1, 0, 0, 0,...
0, 0, 0, 0, 0, 0,...
0, 0, 0, 0, 0, 0,...
... - Gary W. Adamson, Aug 26 2011
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EXAMPLE
| a(4) = 20 = (8 + 8 + 4) since the top row of M^4 = (8, 8, 4, 0, 0, 0,...)
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MATHEMATICA
| Join[{1, 2, a = 5}, Table[a = 2*a, {n, 0, 40}]] (* From Vladimir Joseph Stephan Orlovsky, June 09 2011 *)
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CROSSREFS
| Cf. A060816.
Sequence in context: A159230 A181366 A068034 * A024810 A049938 A002460
Adjacent sequences: A084212 A084213 A084214 * A084216 A084217 A084218
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 19 2003
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