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A079097 Mix odd numbers and squares. 2
1, 1, 3, 4, 5, 9, 7, 16, 9, 25, 11, 36, 13, 49, 15, 64, 17, 81, 19, 100, 21, 121, 23, 144, 25, 169, 27, 196, 29, 225, 31, 256, 33, 289, 35, 324, 37, 361, 39, 400, 41, 441, 43, 484, 45, 529, 47, 576, 49, 625, 51, 676, 53, 729, 55, 784, 57, 841, 59, 900, 61, 961, 63, 1024, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The old entry with this sequence number was a duplicate of A010892.

This sequence is visible in the identity 4/Pi = 1 + 1/(3 + 4/(5 + 9/(7 + 16/(9 + 25/(11 + ...))))) (see the Wolfram Research web site).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Wolfram Research, Pi

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

FORMULA

a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: (1+x^2)*(x^2-x-1)/((x-1)^3*(1+x)^3). - R. J. Mathar, Jan 05 2009

From Colin Barker, Jan 27 2016: (Start)

a(n) = (-1)*((1+n)*(-5-3*(-1)^n+(-1+(-1)^n)*n))/8.

a(n) = n-1 for n even.

a(n) = (n^2+2*n+1)/4 for n odd.

(End)

MAPLE

f:=n->if n mod 2 = 0 then n+1 else ((n+1)/2)^2; fi;

MATHEMATICA

Riffle[2 Range@ Floor[#/2] - 1, Range[#]^2] &@66 (* or *) CoefficientList[Series[(1 + x^2) (x^2 - x - 1)/((x - 1)^3*(1 + x)^3), {x, 0, 64}], x] (* Michael De Vlieger, Jan 27 2016 *)

LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 1, 3, 4, 5, 9}, 70] (* Vincenzo Librandi, Jan 28 2016 *)

PROG

(PARI) Vec((1+x^2)*(x^2-x-1)/((x-1)^3*(1+x)^3) + O(x^100)) \\ Colin Barker, Jan 27 2016

(MAGMA) [(-1)*((1+n)*(-5-3*(-1)^n+(-1+(-1)^n)*n))/8: n in [0..70]]; // Vincenzo Librandi, Jan 28 2016

CROSSREFS

Cf. A086377.

Cf. A088538 for decimal expansion of 4/Pi.

Sequence in context: A302653 A300738 A065336 * A202475 A036710 A098801

Adjacent sequences:  A079094 A079095 A079096 * A079098 A079099 A079100

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 20 2008

STATUS

approved

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Last modified February 20 12:57 EST 2019. Contains 320327 sequences. (Running on oeis4.)