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A003485
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Hurwitz-Radon function at powers of 2.
(Formerly M1086)
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5
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1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 24, 25, 26, 28, 32, 33, 34, 36, 40, 41, 42, 44, 48, 49, 50, 52, 56, 57, 58, 60, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 88, 89, 90, 92, 96, 97, 98, 100, 104, 105, 106, 108, 112, 113, 114, 116, 120, 121, 122, 124
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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REFERENCES
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T. Y. Lam, The Algebraic Theory of Quadratic Forms. Benjamin, Reading, MA, 1973, p. 131.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 0..10000
V Ovsienko and S Tabachnikov, Affine Hopf fibration, arXiv preprint arXiv:1511.08894 [math.AT], 2015.
V. Ovsienko, Serge Tabachnikov, Hopf fibrations and Hurwitz-Radon numbers, Math. Intell. 38 (2016) 11-18
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
D. B. Shapiro, Letter to N. J. A. Sloane, 1974
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
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G.f.: (1 + x + 2*x^2 + 4*x^3) / ((1-x)*(1-x^4)). - Simon Plouffe in his 1992 dissertation
a(n) = ceiling((n+1)/4) + ceiling((n)/4) + 2*ceiling((n-1)/4) + 4*ceiling((n-2)/4). - Johannes W. Meijer, Jun 07 2011
a(n) = a(n-1) + a(n-4) - a(n-5); a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=9. - Harvey P. Dale, Jun 13 2011
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MAPLE
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A003485:= proc(n): ceil((n+1)/4) + ceil((n)/4) + 2*ceil((n-1)/4) + 4*ceil((n-2)/4) end: seq(A003485(n), n=0..62); # Johannes W. Meijer, Jun 07 2011
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MATHEMATICA
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CoefficientList[Series[(1+x+2x^2+4x^3)/((1-x)(1-x^4)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 8, 9}, 71] (* Harvey P. Dale, Jun 13 2011 *)
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PROG
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(Haskell)
a003485 n = a003485_list !! n
a003485_list = 1 : 2 : 4 : 8 : 9 : zipWith (+)
(drop 4 a003485_list) (zipWith (-) (tail a003485_list) a003485_list)
-- Reinhard Zumkeller, Mar 11 2012
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CROSSREFS
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Cf. A003484.
Essentially the same as A047466.
Cf. A008621. - Johannes W. Meijer, Jun 07 2011
Cf. A209675.
Sequence in context: A044952 A352831 A047466 * A072602 A049642 A326713
Adjacent sequences: A003482 A003483 A003484 * A003486 A003487 A003488
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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