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%I #22 Mar 02 2022 09:23:10
%S 1,3,12,16,41,47,96,104,185,195,316,328,497,511,736,752,1041,1059,
%T 1420,1440,1881,1903,2432,2456,3081,3107,3836,3864,4705,4735,5696,
%U 5728,6817,6851,8076,8112,9481,9519,11040,11080,12761,12803,14652,14696,16721
%N a(1)=1, a(n)=a(n-1)+n if n even, a(n)=a(n-1)+ n^2 if n is odd.
%C The only prime terms are 3, 41, 47.
%C The semiprime terms are A136048.
%C Cf. A001082/A135370: f(1) = 1, then if n even/odd f(n) = n+f(n-1), if n odd/even f(n) = 2*n+f(n-1).
%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 a(n) = (1/12)(1 + n)(2n^2+7n-3) if n is odd, a(n)=(1/12)n(2n^2+3n+4) if n is even.
%F a(n) = (-3 + 3*(-1)^n + 8*n + 12*n^2 - 6*(-1)^n*n^2 + 4*n^3)/24.
%F a(1)=1 then a(n) = a(n-1)+n^(if n is even then 1 else 2),
%F or a(n) = a(n-1)+n^(1+mod(n,2)),
%F or a(n) = a(n-1)+n^((3-(-1)^n)/2)).
%F a(n) = a(n-1)+3a(n-2)-3a(n-3)-3a(n-4)+3a(n-5)+a(n-6)-a(n-7). G.f.: x*(1+2*x+6*x^2-2*x^3+x^4)/((1+x)^3*(x-1)^4). [_R. J. Mathar_, Feb 22 2009]
%t a[1]=1;a[n_]:=a[n]=a[n-1]+n^(1+Mod[n,2]); Table[a[n],{n,100}]
%t nxt[{n_,a_}]:={n+1,If[OddQ[n],a+n+1,a+(n+1)^2]}; Transpose[NestList[nxt,{1,1},50]][[2]] (* _Harvey P. Dale_, Oct 11 2015 *)
%Y Cf. A001082, A135370, A136048.
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Dec 12 2007
%E Edited by _Michel Marcus_, Mar 02 2022
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