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A226008 a(0) = 0; for n>0, a(n) = denominator(1/4 - 4/n^2). 6
0, 4, 4, 36, 1, 100, 36, 196, 16, 324, 100, 484, 9, 676, 196, 900, 64, 1156, 324, 1444, 25, 1764, 484, 2116, 144, 2500, 676, 2916, 49, 3364, 900, 3844, 256, 4356, 1156, 4900, 81, 5476, 1444, 6084, 400, 6724, 1764, 7396, 121, 8100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numerators are in A225948.

Repeated terms of A016826 are in the positions 1, 2, 3, 6, 5, 10, ... (A043547).

LINKS

Table of n, a(n) for n=0..45.

FORMULA

a(n)    = 3*a(n-8) -3*a(n-16) +a(n-24).

a(8n)   = A016802(n), a(8n+4) = A016754(n).

a(4n)   = A154615(n).

a(4n+1) = A017090(n).

a(4n+2) = a(2n+1) = A016826(n); a(2n) = A061038(n).

a(4n+3) = A017138(n).

G.f.: x*(4 +4*x +36*x^2 +x^3 +100*x^4 +36*x^5 +196*x^6 +16*x^7 +312*x^8 +88*x^9 +376*x^10 +6*x^11 +376*x^12 +88*x^13 +312*x^14 +16*x^15 +196*x^16 +36*x^17 +100*x^18 +x^19 +36*x^20 +4*x^21 +4*x^22)/(1-x^8)^3. [Bruno Berselli, May 23 2013]

a(n) = n^2*(6*cos(3*Pi*n/4)+6*cos(Pi*n/4)-54*cos(Pi*n/2)-219*(-1)^n+293)/128. [Bruno Berselli, May 23 2013]

a(n+9) = a(n+1)*((n+9)/(n+1))^2. [Bruno Berselli, May 23 2013]

EXAMPLE

a(0)=(-1+1)^2=0, a(1)=(-3+5)^2=4, a(2)=(-1+3)^2=4.

MATHEMATICA

Join[{0}, Table[Denominator[1/4 - 4/n^2], {n, 49}]] (* Alonso del Arte, May 22 2013 *)

PROG

(MAGMA) [0] cat [Denominator(1/4-4/n^2): n in [1..50]]; // Bruno Berselli, May 23 2013

CROSSREFS

Cf. A016754, A016802, A016826, A017090, A017138, A154615, A225948.

Cf. A225975 (associated square roots).

Sequence in context: A089542 A222285 A222504 * A145109 A181858 A227511

Adjacent sequences:  A226005 A226006 A226007 * A226009 A226010 A226011

KEYWORD

nonn,frac,easy

AUTHOR

Paul Curtz, May 22 2013

EXTENSIONS

Edited by Bruno Berselli, May 23 2013

STATUS

approved

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Last modified June 16 21:20 EDT 2019. Contains 324155 sequences. (Running on oeis4.)