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 A077957 Powers of 2 alternating with zeros. 54
 1, 0, 2, 0, 4, 0, 8, 0, 16, 0, 32, 0, 64, 0, 128, 0, 256, 0, 512, 0, 1024, 0, 2048, 0, 4096, 0, 8192, 0, 16384, 0, 32768, 0, 65536, 0, 131072, 0, 262144, 0, 524288, 0, 1048576, 0, 2097152, 0, 4194304, 0, 8388608, 0, 16777216, 0, 33554432, 0, 67108864, 0, 134217728, 0, 268435456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database. Inverse binomial transform of A001333. - Paul Barry, Feb 25 2003 "Sloping binary representation" of powers of 2 (A000079), slope=-1 (see A037095 and A102370). - Philippe Deléham, Jan 04 2008 0,1,0,2,0,4,0,8,0,16,... is the inverse binomial transform of A000129 (Pell numbers). - Philippe Deléham, Oct 28 2008 Number of maximal self-avoiding walks from the NW to SW corners of a 3 X n grid. Row sums of the triangle in A204293. - Reinhard Zumkeller, Jan 14 2012 Pisano period lengths: 1, 1, 4, 1, 8, 4, 6, 1, 12, 8, 20, 4, 24, 6, 8, 1, 16, 12, 36, 8, ... . - R. J. Mathar, Aug 10 2012 This sequence occurs in the length L(n) = sqrt(2)^n of Lévy's C-curve at the n-th iteration step. Therefore, L(n) is the Q(sqrt(2)) integer a(n) + a(n-1)*sqrt(2), with a(-1) = 0. For a variant of this C-curve see A251732 and A251733. - Wolfdieter Lang, Dec 08 2014 a(n) counts walks (closed) on the graph G(1-vertex,2-loop,2-loop). Equivalently the middle entry (2,2) of A^n where the adjacency matrix of digraph is A=(0,1,0;1,0,1;0,1,0). - David Neil McGrath, Dec 19 2014 a(n-2) is the number of compositions of n into even parts. For example, there are 4 compositions of 6 into even parts: (6), (222), (42), and (24). - David Neil McGrath, Dec 19 2014 Also the number of alternately constant compositions of n + 2, ranked by A351010. The alternately strict version gives A000213. The unordered version is A035363, ranked by A000290, strict A035457. - Gus Wiseman, Feb 19 2022 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,2). FORMULA G.f.: 1/(1-2*x^2). E.g.f.: cosh(x*sqrt(2)). a(n) = (1 - n mod 2) * 2^floor(n/2). a(n) = sqrt(2)^n*(1+(-1)^n)/2. - Paul Barry, May 13 2003 a(n) = 2*a(n-2) with a(0)=1, a(1)=0. - Jim Singh, Jul 12 2018 MAPLE seq(op([2^n, 0]), n=0..100); # Robert Israel, Dec 23 2014 MATHEMATICA a077957[n_] := Riffle[Table[2^i, {i, 0, n - 1}], Table[0, {n}]]; a077957[29] (* Michael De Vlieger, Dec 22 2014 *) CoefficientList[Series[1/(1 - 2*x^2), {x, 0, 50}], x] (* G. C. Greubel, Apr 12 2017 *) LinearRecurrence[{0, 2}, {1, 0}, 54] (* Robert G. Wilson v, Jul 23 2018 *) Riffle[2^Range[0, 30], 0, {2, -1, 2}] (* Harvey P. Dale, Jan 06 2022 *) PROG (PARI) a(n)=if(n<0||n%2, 0, 2^(n/2)) (Haskell) a077957 = sum . a204293_row -- Reinhard Zumkeller, Jan 14 2012 (Sage) def A077957(): x, y = -1, 1 while True: yield -x x, y = x + y, x - y a = A077957(); [next(a) for i in range(40)] # Peter Luschny, Jul 11 2013 (Magma) &cat [[2^n, 0]: n in [0..20]]; // Vincenzo Librandi, Apr 03 2018 (GAP) Flat(List([0..30], n->[2^n, 0])); # Muniru A Asiru, Aug 05 2018 CROSSREFS Cf. A000079, A077966. Column k=3 of A219946. - Alois P. Heinz, Dec 01 2012 Cf. A016116 (powers repeated). Sequence in context: A349232 A194795 A131575 * A077966 A275670 A021102 Adjacent sequences: A077954 A077955 A077956 * A077958 A077959 A077960 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 17 2002 STATUS approved

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Last modified December 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)