This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A271115 #71 Sep 01 2025 19:47:40
%S A271115 1,50049,410924801,491565199,4035971329551,33137139500710799,
%T A271115 39640013290309201,325462334331581751249,2672192117918839703333201,
%U A271115 3196586448455823020136799,26245412174507812354285027551,215486635921438132237851754543199
%N A271115 Numbers whose square is a chiliagonal (or 1000-gonal) number.
%C A271115 a(n) is odd since a(n) mod 10 = 1 or 9. Since all odd numbers with one or two distinct prime factors are deficient, a(n) is deficient. E.g., 7294309908480 = sigma(a(5)) < 2*a(5) = 8071942659102. - _Muniru A Asiru_, Nov 17 2016
%C A271115 The digital root of a(3*n) is A131598(n-1). - _Muniru A Asiru_, Dec 01 2016
%H A271115 Colin Barker, <a href="/A271115/b271115.txt">Table of n, a(n) for n = 1..350</a>
%H A271115 M. A. Asiru, <a href="http://dx.doi.org/10.1080/0020739X.2016.1164346">All square chiliagonal numbers</a>, Int J Math Edu Sci Technol, 47:7(2016), 1123-1134.
%H A271115 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,80640398,0,0,-1).
%F A271115 a(n)^2 = A271105(n).
%F A271115 a(n) = 80640398*a(n-3)-a(n-6) for n>6. - _Colin Barker_, Apr 01 2016
%F A271115 G.f.: x*(1+x)*(1+50048*x+410874753*x^2+50048*x^3+x^4) / (1-80640398*x^3+x^6). - _Colin Barker_, Apr 01 2016
%F A271115 a(n) = 40320199*a(n-3) + 900685020*A271470(n-3) - 449440020 for n>3. - _Muniru A Asiru_, Apr 09 2016
%F A271115 A010888(a(3*n)) = A131598(n-1) where A131598 has period 3: repeat [2, 5, 8] and A010888 is digital root. - _Michel Marcus_, Dec 04 2014
%e A271115 50049 is in the sequence because 50049^2 = 2504902401, which is the 2241st 1000-gonal number. - _Colin Barker_, Apr 01 2016
%t A271115 Rest@ CoefficientList[Series[x (1 + x) (1 + 50048 x + 410874753 x^2 + 50048 x^3 + x^4)/(1 - 80640398 x^3 + x^6), {x, 0, 12}], x] (* _Michael De Vlieger_, Apr 01 2016 *)
%t A271115 LinearRecurrence[{0,0,80640398,0,0,-1},{1,50049,410924801,491565199,4035971329551,33137139500710799},20] (* _Harvey P. Dale_, Sep 01 2025 *)
%o A271115 (PARI) Vec(x*(1+x)*(1+50048*x+410874753*x^2+50048*x^3+x^4)/(1-80640398*x^3+x^6) + O(x^15)) /* _Colin Barker_, Apr 01 2016 */
%o A271115 (GAP)
%o A271115 g:=1000; Q0:=(g-4)^2; D1:=2*g-4;
%o A271115 S:=[2*[ 500, 1 ], 4*[ 1022201, 22880 ], 498*[ 8980, 201 ], 996*[ 1, 0 ],-2*[- 500, 1 ], -4*[- 1022201, 22880 ]];;
%o A271115 S1:=Filtered(S,i->IsInt((i[1]+g-4)/(2*g-4)));;
%o A271115 S2:=Filtered([1..Length(S)],i->IsInt((S[i][1]+g-4)/(2*g-4)));;
%o A271115 S3:=List(S2,i->S[i]);;
%o A271115 u:=40320199;; v:=902490;; G:=[[u,2*(g-2)*v],[v,u]];;
%o A271115 A:=List([1..Length(S3)],s->List(List([0..6],i->G^i*TransposedMat([S3[s]])),Concatenation));; Length(A);
%o A271115 D1:=Union(List([1..Length(A)],k->A[k]));; Length(D1);
%o A271115 D2:=List(D1,i-> [(i[1]+(g-4))/(2*(g-2)),i[2]/2] );; Length(D2);
%o A271115 D3:=Filtered(D2,i->IsInt(i[1]));
%o A271115 D4:=Filtered(D3,i->i[2]>0);
%o A271115 D5:=List(D4,i->i[2]); # indices of square numbers for square 1000 gonal numbers (or square chiliagonal numbers)
%Y A271115 Cf. A000290, A195163, A271105.
%K A271115 nonn,easy,changed
%O A271115 1,2
%A A271115 _Muniru A Asiru_, Mar 31 2016
%E A271115 Merged with identical sequence submitted by _Colin Barker_, Apr 01 2016. - _N. J. A. Sloane_, Apr 06 2016