|
%I #39 Jan 13 2024 03:33:31
%S 1,5,35,51,117,145,247,287,425,477,651,715,925,1001,1247,1335,1617,
%T 1717,2035,2147,2501,2625,3015,3151,3577,3725,4187,4347,4845,5017,
%U 5551,5735,6305,6501,7107,7315,7957,8177,8855,9087,9801,10045,10795,11051,11837
%N Odd pentagonal numbers.
%H Vincenzo Librandi, <a href="/A014632/b014632.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -2, -1, 1).
%F a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).
%F a(n) = 48+2*a(n-2)-a(n-4). - _Ant King_, Aug 16 2011
%F G.f.: (1+4*x+28*x^2+8*x^3+7*x^4)/((1+x)^2*(1-x)^3). - _R. J. Mathar_, Jul 25 2009
%F a(n) = (3*(-1)^n+12*n+1)*((-1)^n+4*n+1)/8. - _Ant King_, Aug 16 2011
%F Sum_{n>=0} 1/a(n) = Pi/4 + 3*log(3)/2 + sqrt(3)*log(2-sqrt(3))/2. - _Amiram Eldar_, Jan 13 2024
%p A014632:=n->(3*(-1)^n+12*n+1)*((-1)^n+4*n+1)/8: seq(A014632(n), n=0..100); # _Wesley Ivan Hurt_, Apr 28 2017
%t Select[Table[n (3 n - 1)/2, {n,100}], OddQ] (* _Harvey P. Dale_, Feb 03 2011 *)
%o (Magma) [1/8*(11+3*(-1)^(n+1)-12*(n+1))*(3+(-1)^(n+1)-4*(n+1)): n in [0..40]]; // _Vincenzo Librandi_, Aug 17 2011
%Y Cf. A000326, A014633.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_
%E More terms from _Patrick De Geest_
|
