%I #17 Jul 21 2021 13:19:36

%S 1,5,18,63,221,776,2725,9569,33602,117995,414345,1454992,5109273,

%T 17941453,63002258,221235399,776878533,2728045592,9579660701,

%U 33639430153,118126444802,414806579603,1456612858961,5114964721440,17961439747441,63072442405845,221481854849938,777743974335503,2731084630047981

%N "INVERT" transform of squares A000290.

%C Number of compositions of n+1 whose parts equal to q can be of q^2 kinds. Example: a(1)=5 because we have (2),(2'),(2"),(2'") and (1,1). Row sums of A105495. - _Emeric Deutsch_, Apr 10 2005

%H Colin Barker, <a href="/A033453/b033453.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,1).

%F G.f.: (1 + x) / (1 - 4*x + 2*x^2 - x^3).

%F a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) for n>2. - _Colin Barker_, Mar 19 2019

%p read transforms; [seq(n^2,n=1..50)]; INVERT(%);

%t nn=20;a=(x+x^2)/(1-x)^3;Drop[CoefficientList[Series[1/(1-a),{x,0,nn}],x],1] (* _Geoffrey Critzer_, Aug 31 2012*)

%o (PARI) Vec((1 + x) / (1 - 4*x + 2*x^2 - x^3) + O(x^30)) \\ _Colin Barker_, Mar 19 2019

%Y Cf. A105495.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.