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 A079977 Fibonacci numbers interspersed with zeros. 12
 1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 8, 0, 13, 0, 21, 0, 34, 0, 55, 0, 89, 0, 144, 0, 233, 0, 377, 0, 610, 0, 987, 0, 1597, 0, 2584, 0, 4181, 0, 6765, 0, 10946, 0, 17711, 0, 28657, 0, 46368, 0, 75025, 0, 121393, 0, 196418, 0, 317811, 0, 514229, 0, 832040, 0, 1346269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=3, I={0,2}. Number of compositions of n into elements of the set {2,4}. a(n-2) is the number of circular arrangements of the first n positive integers such that adjacent terms have absolute difference 1 or 3. - Ethan Patrick White, Jun 24 2020 REFERENCES D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135. Ethan P. White, Richard K. Guy, and Renate Scheidler, Difference Necklaces, arXiv:2006.15250 [math.CO], 2020. Index entries for linear recurrences with constant coefficients, signature (0,1,0,1). FORMULA a(n) = A000045(k+1) if n=2k, a(n)=0 otherwise. a(n) = a(n-2) + a(n-4). G.f.: 1/(1 - x^2 - x^4). MATHEMATICA Riffle[Fibonacci[Range[50]], 0] (* Harvey P. Dale, Dec 20 2015 *) PROG (PARI) a(n)=if(n%2, 0, fibonacci(n/2+1)) \\ Charles R Greathouse IV, Jun 11 2015 (Magma) A079977:= func< n | (1+(-1)^n)*Fibonacci(Floor((n+2)/2))/2 >; [A079977(n): n in [0..50]]; // G. C. Greubel, Jul 25 2022 (SageMath) def A079977(n): return ((n+1)%2)*fibonacci((n+2)//2) [A079977(n) for n in (0..50)] # G. C. Greubel, Jul 25 2022 CROSSREFS Cf. A000045, A002524, A002525, A002526, A002527, A002528, A002529, A072827. Cf. A072850, A072851, A072852, A072853, A072854, A072855, A072856, A099574. Cf. A079955 - A080014. Sequence in context: A035363 A241645 A266774 * A227093 A266772 A262064 Adjacent sequences: A079974 A079975 A079976 * A079978 A079979 A079980 KEYWORD nonn,easy AUTHOR Vladimir Baltic, Feb 17 2003 EXTENSIONS Editorial note: normally the alternate zeros are omitted from sequences like this. This entry is an exception. - N. J. A. Sloane STATUS approved

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Last modified April 21 14:30 EDT 2024. Contains 371874 sequences. (Running on oeis4.)