|
%I #27 Aug 01 2015 13:57:15
%S 0,1,10,44,341,1495,11584,50786,393515,1725229,13367926,58607000,
%T 454115969,1990912771,15426575020,67632427214,524049434711,
%U 2297511612505,17802254205154,78047762397956,604752593540525,2651326409917999,20543785926172696,90067050174814010
%N Indices of square numbers that are also 18-gonal numbers.
%C Solving the Diophantine equation A051870(m) = m*(8*m-7) = k^2 leads to the entries.
%C k in the sequence and a list of associated m = 0, 1, 4, 16, 121, 529, 4096, 17956, 139129, 609961...
%H Colin Barker, <a href="/A160970/b160970.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,34,0,-1).
%F a(n) = 34*a(n-2) - a(n-4), n>5. - _R. J. Mathar_, Oct 04 2009
%F G.f.: x^2*(x+1)*(x^2 + 9*x + 1)/((x^2 - 6*x + 1)*(x^2 + 6*x + 1)). - _Colin Barker_, Oct 07 2012
%F For all values excepting the leading 0, a(n) = sqrt(8*A006452(n)^2 - 7)*A006452(n) = sqrt(A006451(n-1)*(A006451(n-1) + 1)/2 + 1)*(2*A006451(n-1) + 1). - _Raphie Frank_, Feb 11 2013
%t Join[{0},LinearRecurrence[{0,34,0,-1},{1,10,44,340},23]] (* _Ray Chandler_, Aug 01 2015 *)
%o (PARI) is(n)=ispolygonal(n^2,18) \\ _Charles R Greathouse IV_, Feb 14 2013
%o (PARI) concat(0, Vec(x^2*(x+1)*(x^2+9*x+1)/((x^2-6*x+1)*(x^2+6*x+1)) + O(x^50))) \\ _Colin Barker_, Jun 24 2015
%Y Cf. A006451, A006452.
%K nonn,easy
%O 1,3
%A _Sture Sjöstedt_, Jun 01 2009, Jul 02 2009
%E 0 added in front and extended by _R. J. Mathar_, Oct 04 2009
|
