cp's OEIS Frontend

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.

A254283 Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).

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%I A254283 #7 Jun 13 2015 00:55:23
%S A254283 1,31,115,5965,22261,1157131,4318471,224477401,837761065,43547458615,
%T A254283 162521328091,8447982493861,31528299888541,1638865056350371,
%U A254283 6116327657048815,317931372949478065,1186536037167581521,61677047487142394191,230181874882853766211
%N A254283 Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).
%C A254283 Also positive integers x in the solutions to 4*x^2 - 3*y^2 - 2*x + 3*y - 2 = 0, the corresponding values of y being A254284.
%H A254283 Colin Barker, <a href="/A254283/b254283.txt">Table of n, a(n) for n = 1..875</a>
%H A254283 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,194,-194,-1,1).
%F A254283 a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).
%F A254283 G.f.: -x*(x^4+30*x^3-110*x^2+30*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).
%e A254283 31 is in the sequence because the 31st hexagonal number is 1891, which is also the 36th centered triangular number.
%o A254283 (PARI) Vec(-x*(x^4+30*x^3-110*x^2+30*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))
%Y A254283 Cf. A000384, A005448, A254284, A254285.
%K A254283 nonn,easy
%O A254283 1,2
%A A254283 _Colin Barker_, Jan 28 2015