# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a006062
Showing 1-1 of 1

%I A006062 M5265 #52 Sep 02 2024 08:38:02
%S A006062 1,37,1261,42841,1455337,49438621,1679457781,57052125937,
%T A006062 1938092824081,65838103892821,2236557439531837,75977114840189641,
%U A006062 2580985347126915961,87677524687474953037,2978454854027021487301,101179787512231255615201,3437134320561835669429537
%N A006062 Star-hex numbers.
%D A006062 Martin Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 22.
%D A006062 Harvey J. Hindin, Stars, hexes, triangular numbers and Pythagorean triples, J. Rec. Math., 16 (1983/1984), 191-193.
%D A006062 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006062 Paolo Xausa, <a href="/A006062/b006062.txt">Table of n, a(n) for n = 1..650</a>
%H A006062 Harvey 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 A006062 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 A006062 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A006062 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35,-35,1).
%F A006062 a(n) = 34*a(n-1) - a(n-2) + 4.
%F A006062 G.f.: -x*(x + 1)^2/(x - 1)/(x^2 - 34*x + 1). [from _Simon Plouffe_, see Maple code].
%F A006062 From _Charlie Marion_, Aug 03 2005: (Start)
%F A006062 a(n) = A001109(n-1)^2 + A001109(n)^2; e.g., 1261 = 6^2 + 35^2.
%F A006062 a(n) = A001652(n-1)*A046090(n-1) + A001653(n-1)^2; e.g., 1261 = 20*21 + 29^2. (End)
%p A006062 A006062:=-(z+1)**2/(z-1)/(z**2-34*z+1); [_Simon Plouffe_ in his 1992 dissertation for offset zero.]
%t A006062 LinearRecurrence[{35, -35, 1}, {1, 37, 1261}, 20] (* _Paolo Xausa_, Sep 02 2024 *)
%Y A006062 Cf. A001109, A001652, A001653, A046090.
%K A006062 nonn,easy
%O A006062 1,2
%A A006062 _N. J. A. Sloane_, Jul 11 1991

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE