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A003485 Hurwitz-Radon function at powers of 2.
(Formerly M1086)
5
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)
OFFSET

0,2

REFERENCES

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).

LINKS

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 and Conjectures, Université du Québec à Montréal, 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).

FORMULA

G.f.: (1+x+2*x^2+4*x^3) / ((1-x)*(1-x^4)). - Simon Plouffe in his 1992 dissertation

a(n) = ceil((n+1)/4) + ceil((n)/4) + 2*ceil((n-1)/4) + 4*ceil((n-2)/4). - Johannes W. Meijer, Jun 07 2011

a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=9, a(n)=a(n-1)+a(n-4)-a(n-5). - Harvey P. Dale, Jun 13 2011

MAPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

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 A050907

Adjacent sequences:  A003482 A003483 A003484 * A003486 A003487 A003488

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 22 03:08 EDT 2019. Contains 321406 sequences. (Running on oeis4.)