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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, S Tabachnikov, Affine Hopf fibration, arXiv preprint arXiv:1511.08894, 2015
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
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: A196000 A044952 A047466 * A072602 A049642 A326713
Adjacent sequences: A003482 A003483 A003484 * A003486 A003487 A003488
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KEYWORD
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easy,nonn,nice,changed
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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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