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%I #26 Aug 02 2023 07:13:49
%S 1,5,55,91,285,385,819,1015,1785,2109,3311,3795,5525,6201,8555,9455,
%T 12529,13685,17575,19019,23821,25585,31395,33511,40425,42925,51039,
%U 53955,63365,66729,77531,81375,93665,98021,111895,116795,132349,137825,155155,161239,180441
%N Odd square pyramidal numbers.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F Odd numbers in A000330.
%F From _Ant King_, Oct 17 2012: (Start)
%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + 128.
%F a(n) = (1 + 4*n + (-1)^n)*(2 + 4*n + (-1)^n)*(3 + 4*n + (-1)^n)/24.
%F G.f.: (1+4*x+47*x^2+24*x^3+47*x^4+4*x^5+x^6)/((1-x)^4*(1+x)^3). (End)
%F From _Amiram Eldar_, Mar 07 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 6*sqrt(2)*log(sqrt(2)+1) - 9*log(2).
%F Sum_{n>=0} (-1)^n/a(n) = 3*Pi*(1-2*tan(Pi/8))/2. (End)
%t LinearRecurrence[{1,3,-3,-3,3,1,-1}, {1,5,55,91,285,385,819}, 38] (* _Ant King_ Oct 17 2012 *)
%Y Cf. A000330, A015222.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_
%E More terms from _Erich Friedman_