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%I M5265 #45 Jul 02 2023 13:43:42
%S 1,37,1261,42841,1455337,49438621,1679457781,57052125937,
%T 1938092824081,65838103892821,2236557439531837,75977114840189641,
%U 2580985347126915961,87677524687474953037,2978454854027021487301,101179787512231255615201
%N Star-hex numbers.
%D M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 22.
%D H. J. Hindin, Stars, hexes, triangular numbers and Pythagorean triples, J. Rec. Math., 16 (1983/1984), 191-193.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H H. J. Hindin, <a href="/A006062/a006062.pdf">Stars, hexes, triangular numbers and Pythagorean triples</a>, J. Rec. Math., 16 (1983/1984), 191-193. (Annotated scanned copy)
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35, -35, 1).
%F a(n) = 34*a(n-1) - a(n-2) + 4.
%F G.f.: -x*(x + 1)^2/(x - 1)/(x^2 - 34*x + 1). [from _Simon Plouffe_, see Maple code].
%F From _Charlie Marion_, Aug 03 2005: (Start)
%F a(n) = A001109(n-1)^2 + A001109(n)^2; e.g., 1261 = 6^2 + 35^2.
%F a(n) = A001652(n-1)*A046090(n-1) + A001653(n-1)^2; e.g., 1261 = 20*21 + 29^2. (End)
%p A006062:=-(z+1)**2/(z-1)/(z**2-34*z+1); [_Simon Plouffe_ in his 1992 dissertation for offset zero.]
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jul 11 1991
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