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%I #29 Feb 27 2022 05:46:58
%S 1,225,2025,8281,23409,53361,105625,189225,314721,494209,741321,
%T 1071225,1500625,2047761,2732409,3575881,4601025,5832225,7295401,
%U 9018009,11029041,13359025,16040025,19105641,22591009,26532801,30969225,35940025,41486481,47651409
%N Squares of odd hexagonal numbers.
%H Vincenzo Librandi, <a href="/A014771/b014771.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: x*(1+220*x+910*x^2+396*x^3+9*x^4)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by _R. J. Mathar_, Sep 16 2009
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. - _Harvey P. Dale_, Jun 23 2011
%F a(n) = (2*n-1)^2*(4*n-3)^2. - _Wesley Ivan Hurt_, Jul 31 2016
%F Sum_{n>=1} 1/a(n) = 2*G + 3*Pi^2/8 - Pi - 2*log(2), where G is Catalan's constant (A006752). - _Amiram Eldar_, Feb 27 2022
%p A014771:=n->(2*n-1)^2*(4*n-3)^2: seq(A014771(n), n=1..50); # _Wesley Ivan Hurt_, Jul 31 2016
%t (Select[Table[n(2n-1), {n,60}], OddQ])^2 (* or *) LinearRecurrence[ {5,-10,10,-5,1}, {1,225,2025,8281,23409}, 30] (* _Harvey P. Dale_, Jun 23 2011 *)
%o (Magma) [(2*n-1)^2*(4*n-3)^2 : n in [1..50]]; // _Wesley Ivan Hurt_, Jul 31 2016
%Y Cf. A003215, (hex numbers), A014634 (odd hex numbers), A006752.
%K nonn,easy
%O 1,2
%A _Mohammad K. Azarian_
%E More terms from _Erich Friedman_