This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A227168 Squares of gcd( 2*n, n*(n+1)/2 ). 1
 1, 1, 36, 4, 25, 9, 196, 16, 81, 25, 484, 36, 169, 49, 900, 64, 289, 81, 1444, 100, 441, 121, 2116, 144, 625, 169, 2916, 196, 841, 225, 3844, 256, 1089, 289, 4900, 324, 1369, 361, 6084, 400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is defined as A062828(n)^2 for n >= 1. If we extend the sequence to n=0 and negative n by use of the recurrence that relates a(n) to a(n+12), a(n+8) and a(n+4), we obtain a(0)=0, a(-1)=4 and a(-n) = A176743(n-2)^2 for n >= 2. Define c(n) = a(n+2) - a(n-2) for c >= 0. Because a(n) is a shuffle of three interleaved 2nd order polynomials, c(n) is a shuffle of three interleaved 1st order polynomials: c(n) = 4* A062828(n)*(periodically repeated 1, 8, 1, 1). The sequence a(n) is case p=0 of the family A062828(n)*A062828(n+p): 0, 1, 1, 36,  4, 25,  9, 196, ... = a(n). 0, 1, 6, 12, 10, 15, 42,  56, ... = A130658(n)*A000217(n) = A177002(n-1)*A064038(n+1). 0, 6, 2, 30,  6, 70, 12, 126, ... = 2*A198148(n) 0, 2, 5, 18, 28, 20, 27,  70, ... = A177002(n+2)*A160050(n+1) = A014695(n+2)*A000096(n). LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1). FORMULA a(n) = A062828(n)^2. a(4n) = (4*n+1)^2; a(2n+1) = (n+1)^2; a(4n+2) = 4*(4*n+3)^2. a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12). a(n) * (period 4: repeat 4, 1, 1, 4) = A061038(n). A005565(n-3) = a(n+1) * A061037(n). - Corrected by R. J. Mathar, Jul 25 2013 a(n) = A130658(n-1)^2 * A181318(n). - Corrected by R. J. Mathar, Aug 01 2013 G.f.: -x*(1 + x + 36*x^2 + 4*x^3 + 22*x^4 + 6*x^5 + 88*x^6 + 4*x^7 + 9*x^8 + x^9 + 4*x^10) / ( (x-1)^3*(1+x)^3*(x^2+1)^3 ). - R. J. Mathar, Jul 20 2013 MAPLE A227168 := proc(n)     A062828(n)^2 ; end proc: # R. J. Mathar, Jul 25 2013 MATHEMATICA a[n_] := GCD[2*n, n*(n + 1)/2]^2; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 03 2013 *) PROG (PARI) a(n)=if(n%2, n*if(n%4>2, 2, 1), n/2)^2 \\ Charles R Greathouse IV, Jul 07 2013 (MAGMA) [GCD(2*n, n*(n+1)/2)^2: n in [1..50]]; // G. C. Greubel, Sep 20 2018 CROSSREFS Cf. A062828, A016814, A017138, A005565, A061037, A061038. Sequence in context: A037935 A159824 A285575 * A100252 A020340 A255868 Adjacent sequences:  A227165 A227166 A227167 * A227169 A227170 A227171 KEYWORD nonn,easy,less AUTHOR Paul Curtz, Jul 03 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)