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A131174 a(2n) = 2*A000217(n), a(2n+1) = A000217(n).

%I A131174 #20 Jun 25 2022 22:52:58
%S A131174 0,0,2,1,6,3,12,6,20,10,30,15,42,21,56,28,72,36,90,45,110,55,132,66,
%T A131174 156,78,182,91,210,105,240,120,272,136,306,153,342,171,380,190,420,
%U A131174 210,462,231,506,253,552,276,600,300,650,325,702,351,756,378,812,406,870,435
%N A131174 a(2n) = 2*A000217(n), a(2n+1) = A000217(n).
%H A131174 Harvey P. Dale, <a href="/A131174/b131174.txt">Table of n, a(n) for n = 0..1000</a>
%H A131174 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 3, 0, -3, 0, 1).
%F A131174 a(n) = 3*a(n-2)-3*a(n-4)+a(n-6).
%F A131174 G.f.: x^2*(2+x)/((1-x)^3*(1+x)^3). [_R. J. Mathar_, Jul 17 2009]
%F A131174 a(n) = (3*n^2+4*n-1+(n^2+4*n+1)*(-1)^n)/16. - _Luce ETIENNE_, Aug 19 2014
%p A131174 A000217 := proc(n) n*(n+1)/2 ; end: A131174 := proc(n) if n mod 2 = 0 then 2*A000217(n/2) ; else A000217((n-1)/2) ; fi ; end: seq(A131174(n),n=0..90) ; # _R. J. Mathar_, Oct 26 2007
%t A131174 LinearRecurrence[{0,3,0,-3,0,1},{0,0,2,1,6,3},60] (* _Harvey P. Dale_, Jun 01 2012 *)
%Y A131174 Partial sums of A131119.
%K A131174 nonn
%O A131174 0,3
%A A131174 _Paul Curtz_, Sep 24 2007
%E A131174 Edited by _N. J. A. Sloane_, Sep 27 2007
%E A131174 More terms from _R. J. Mathar_, Oct 26 2007