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A165665
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a(n) = (3*2^n - 2) * 2^n.
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5
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1, 8, 40, 176, 736, 3008, 12160, 48896, 196096, 785408, 3143680, 12578816, 50323456, 201310208, 805273600, 3221159936, 12884770816, 51539345408, 206157905920, 824632672256, 3298532786176, 13194135339008, 52776549744640
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A058481. Second binomial transform of (A082505 without initial term 0). Third binomial transform of A010686.
a(n) is the sum of the odd numbers taken progressively by moving through them by 2^n-tuples. a(0)=1; a(1) = 3+5=8; a(2) = 7+9+11+13 = 40; a(3) = 15+17+19+21+23+25+27+29 = 176; a(n) = sum_{k=0,1,..,A000225(n)} (A000225(n+1)+2*k). - J. M. Bergot, Dec 06 2014
The number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 773", based on the 5-celled von Neumann neighborhood. - Robert Price, May 23 2016
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LINKS
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FORMULA
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a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
G.f.: (2*x+1)/((1-2*x)*(1-4*x)).
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MATHEMATICA
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Table[(3*2^n-2)2^n, {n, 0, 30}] (* or *) LinearRecurrence[{6, -8}, {1, 8}, 30] (* Harvey P. Dale, Nov 18 2020 *)
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PROG
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(Magma) [ (3*2^n-2)*2^n: n in [0..23] ];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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