%I #14 Sep 08 2022 08:46:13
%S 1,106,345,122130,397937,140937722,459218761,162642008866,
%T 529938052065,187688737293450,611548052864057,216592640194632242,
%U 705725923067069521,249947719095868313626,814407103671345362985,288439451243991839291970
%N Indices i of pentagonal numbers P(i) such that (P(i)-1)/2 is also a pentagonal number.
%C Companion sequence to A174685.
%H Ray Chandler, <a href="/A260937/b260937.txt">Table of n, a(n) for n = 1..653</a> (terms to 1000 digits)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1154,-1154,-1,1).
%F G.f.: x*(1 + 105*x - 915*x^2 + 615*x^3 + 2*x^4)/((1 - x)*(1 - 34*x + x^2)*(1 + 34*x + x^2)). [_Bruno Berselli_, Aug 05 2015]
%t LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 106, 345, 122130, 397937}, 20] (* _Vincenzo Librandi_, Aug 05 2015 *)
%o See A174685 for PARI program attributed to _Jack Brennen_.
%o (Magma) I:=[1,106,345,122130,397937]; [n le 5 select I[n] else Self(n-1)+1154*Self(n-2)-1154*Self(n-3)-Self(n-4)+Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Aug 05 2015
%Y Cf. A000326, A174685.
%K nonn,easy
%O 1,2
%A _Ray Chandler_, Aug 04 2015