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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 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.)