来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a054318 Showing 1-1 of 1 %I A054318 %S A054318 1,5,45,441,4361,43165,427285,4229681,41869521,414465525,4102785725, %T A054318 40613391721,402031131481,3979697923085,39394948099365, %U A054318 389969783070561,3860302882606241,38213059042991845,378270287547312205 %N A054318 a(n)-th star number (A003154) is a square. %C A054318 A two-way infinite sequence which is palindromic. %C A054318 Also indices of centered hexagonal numbers (A003215) which are also centered square numbers (A001844). -在02×2 ^ - 6×y ^ 2 - 4×x+6*y=0的解中,2015。- Giovanni Lucca -科林巴克尔(J.Calin Bakkyz),02 2015 2015 %D A054 318,在对称透镜和整数序列中刻划的圆链,Forum Geometricorum,第16卷(2016)419-427;http://FuMuGuM.FUA.EDU/FG2016VoMUE16/FG2016VoMUME16.PDFα页=423μ%H A054 318 Colin Barker,n,a(n)n=1…1000的表%H A054 318双向无穷序列索引条目%H A054 318常系数线性递归的索引项, signature (11,-11,1). %F A054318 a(n) = 11*(a(n-1) - a(n-2)) + a(n-3). %F A054318 a(n) = 1/2 + (3 - sqrt(6))/12*(5 + 2*sqrt(6))^n + (3 + sqrt(6))/12*(5 - 2*sqrt(6))^n. %F A054318 From _Michael Somos_, Mar 18 2003: (Start) %F A054318 G.f.: x*(1-6*x+x^2)/((1-x)*(1-10*x+x^2)). %F A054318 12*a(n)*a(n-1) + 4 = (a(n) + a(n-1) + 2)^2. %F A054318 a(n) = a(1-n) = 10*a(n-1) - a(n-2) - 4. %F A054318 a(n) = 12*a(n-1)^2/(a(n-1) + a(n-2)) - a(n-1). %F A054318 a(n) = (a(n-1) + 4)*a(n-1)/a(n-2). (End) %F A054318 From _Peter Bala_, May 01 2012: (Start) %F A054318 a(n+1) = 1 + (1/2)*Sum_{k = 1..n} 8^k*binomial(n+k,2*k). %F A054318 a(n+1) = R(n,4), where R(n,x) is the n-th row polynomial of A211955. %F A054318 a(n+1) = (1/u)*T(n,u)*T(n+1,u) with u = sqrt(3) and T(n,x) the Chebyshev polynomial of the first kind. %F A054318 Sum {k>=0} 1/a(k) = sqrt(3/2). (结尾)%%F A054 318 A00 3154(A(n))=A00 6061(n)。- 10月22日ZAK Seiovz,2012μF F A054 318 A(n)=(4×A(N-1)+A(N-1)^ 2)/A(N-2),n>=3。- _Seiichi Manyama_, Aug 11 2016 %e A054318 a(2) = 5 because the 5th Star number (A003154) 121=11^2 is the 2nd that is a square. %t A054318 CoefficientList[Series[x(1-6x+x^2)/((1-x)(1-10x+x^2)), {x,0,30}], x] (* _Michael De Vlieger_, Aug 11 2016 *) %t A054318 LinearRecurrence[{11,-11,1},{1,5,45},30] (* _Harvey P. Dale_, Nov 05 2016 *) %o A054318 (PARI) a(n)=if(n<1,a(1-n),1/2+subst(poltchebi(n)+poltchebi(n-1),x,5)/12) %o A054318 (PARI) Vec(x*(1-6*x+x^2)/((1-x)*(1-10*x+x^2)) + O(x^30)) \\ _Colin Barker_, Jan 02 2015 %o A054318 (MAGMA) R= PrimeSeriSrin(整数(),30);Coefficients(R)!( x*(1-6*x+x^2)/((1-x)*(1-10*x+x^2)) )); // _G. C. Greubel_, Jul 23 2019 %o A054318 (Sage) (x*(1-6*x+x^2)/((1-x)*(1-10*x+x^2))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 23 2019 %o A054318 (GAP) a:=[1,5,45];; for n in [4..30] do a[n]:=11*a[n-1]-11*a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Jul 23 2019 %Y A054318 A031138 is 3*a(n)-2. A31827,K=2,A000 1844,A000 32 15,A2534 75,K% A054 318易,非N%O O A054 318,1 2 2 %,A054 318,IGANACO LARROSA CA CA,2月27日2000 2000 %E A054 318更多的条款来自于J.J.E.SelesSy,MAR 01 2000‰的内容在OEIS最终用户许可协议下可用:HTTP:/OEIS.Org/许可证A000 3154,A000 6061,A182432,A211955.0%YA0