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%I #20 Jan 02 2024 08:54:00
%S 1,4,16,61,229,856,3196,11929,44521,166156,620104,2314261,8636941,
%T 32233504,120297076,448954801,1675522129,6253133716,23337012736,
%U 87094917229,325042656181,1213075707496,4527260173804,16895964987721
%N Indices of the triangular numbers which are also centered triangular number.
%C Also, indices of the triangular numbers which are sums of three consecutive triangular numbers (see A129803).
%H A. Kozikowska, <a href="http://www.warminski.pollub.plwww.ptmts.org.pl/2011-4-kozikowska.pdf">Topological classes of statically determinate beams with arbitrary number of supports</a>, JOURNAL OF THEORETICAL AND APPLIED MECHANICS 49, 4, pp. 1079-1100, Warsaw 2011; (see Eq. 5.18). - _N. J. A. Sloane_, Dec 17 2011.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,1).
%F a(n+2)=4*a(n+1)-a(n)+1.
%F a(n+1)=2*a(n)+0.5+0.5*(12*a(n)^2+12*a(n)-15)^0.5.
%F G.f.: x*(1-x+x^2)/(1-x)/(1-4*x+x^2). - _R. J. Mathar_, Oct 24 2007
%F a(n)-a(n-1)= A005320(n-1). - _R. J. Mathar_, Mar 14 2016
%t LinearRecurrence[{5,-5,1},{1,4,16},30] (* _Harvey P. Dale_, Aug 29 2017 *)
%Y Cf. A001834, A102871, A128862, A129803, A001571.
%K nonn,easy
%O 1,2
%A _Richard Choulet_, Oct 09 2007
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