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A064108
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a(n) = (20^n - 1)/19.
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39
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0, 1, 21, 421, 8421, 168421, 3368421, 67368421, 1347368421, 26947368421, 538947368421, 10778947368421, 215578947368421, 4311578947368421, 86231578947368421, 1724631578947368421, 34492631578947368421, 689852631578947368421, 13797052631578947368421, 275941052631578947368421
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OFFSET
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0,3
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COMMENTS
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Partial sums of powers of 20 (A009964), q-integers for q=20: diagonal k=1 in triangle A022184.
For n >= 1, a(n) is the total number of holes in a certain box fractal (start with 20 boxes, 1 hole) after n iterations. See illustration in links. - Kival Ngaokrajang, Jan 28 2015
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LINKS
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FORMULA
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a(0)=0, a(1)=1, a(n) = 21*a(n-1) - 20*a(n-2). - Harvey P. Dale, Oct 04 2012
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EXAMPLE
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From N. J. A. Sloane, Nov 04 2014: Can also be obtained by writing powers of 2 in a staggered array and adding them (cf. A249604). For example, a(9) is:
..........1
.........2
........4
.......8
.....16
....32
...64
.128
256
-----------
26947368421
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MAPLE
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a:=n->sum(20^(n-j), j=0..n): seq(a(n), n=0..15); # Zerinvary Lajos, Feb 11 2007
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MATHEMATICA
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(20^Range[20]-1)/19 (* or *) NestList[20#+1&, 1, 20] (* Harvey P. Dale, Oct 04 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 1, 20) for n in range(1, 17)] # Zerinvary Lajos, May 29 2009
(PARI) for (n=0, 100, write("b064108.txt", n, " ", (20^n - 1)/19)) \\ Harry J. Smith, Sep 07 2009
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CROSSREFS
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Cf. A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218722, A064108, A218724, ..., A218733, ..., A218743, ..., A218752, A094028.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Edited and extended to offset 0 by M. F. Hasler, Nov 04 2012
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STATUS
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approved
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