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 A064108 a(n) = (20^n-1)/19. 37
 0, 1, 21, 421, 8421, 168421, 3368421, 67368421, 1347368421, 26947368421, 538947368421, 10778947368421, 215578947368421, 4311578947368421, 86231578947368421, 1724631578947368421, 34492631578947368421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of powers of 20 (A009964), q-integers for q=20: diagonal k=1 in triangle A022184. Partial sums are in A014904  Also, the sequence is related to A014937 by A014937 n) = n*a(n)-sum_{i=0..n-1} a(i), for n>0. - Bruno Berselli, Nov 06 2012 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 LINKS M. F. Hasler, Table of n, a(n) for n = 0..100 Kival Ngaokrajang, Illustration of initial terms Index entries for linear recurrences with constant coefficients, signature (21,-20). FORMULA a(n) = 20*a(n-1) + 1, with a(0)=0. - Vincenzo Librandi, Aug 07 2010 a(0)=0, a(1)=1, a(n) = 21*a(n-1) - 20*a(n-2). - Harvey P. Dale, Oct 04 2012 a(n) = floor(20^n/19). - M. F. Hasler, Nov 04 2012 G.f.: x/((1-x)*(1-20*x)). - Bruno Berselli, Nov 06 2012 EXAMPLE 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 MAPLE a:=n->sum(20^(n-j), j=0..n): seq(a(n), n=0..15); # Zerinvary Lajos, Feb 11 2007 MATHEMATICA (20^Range[20]-1)/19 (* or *) NestList[20#+1&, 1, 20] (* Harvey P. Dale, Oct 04 2012 *) PROG (Sage) [gaussian_binomial(n, 1, 20) for n in xrange(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 (PARI) A064108(n)=20^n\19  \\ M. F. Hasler, Nov 04 2012 (Maxima) A064108(n):=(20^n-1)/19\$ makelist(A064108(n), n, 1, 30); /* Martin Ettl, Nov 05 2012 */ CROSSREFS Cf. A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218722, A064108, A218724, ..., A218733, ..., A218743, ..., A218752, A094028. Cf. also A249604. Sequence in context: A170654 A170702 A170740 * A067895 A215856 A297692 Adjacent sequences:  A064105 A064106 A064107 * A064109 A064110 A064111 KEYWORD nonn,easy AUTHOR Jason Earls, Sep 17 2001 EXTENSIONS Edited and extended to offset 0 by M. F. Hasler, Nov 04 2012 STATUS approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)