A033453 "INVERT" transform of squares A000290.

1, 5, 18, 63, 221, 776, 2725, 9569, 33602, 117995, 414345, 1454992, 5109273, 17941453, 63002258, 221235399, 776878533, 2728045592, 9579660701, 33639430153, 118126444802, 414806579603, 1456612858961, 5114964721440, 17961439747441, 63072442405845, 221481854849938, 777743974335503, 2731084630047981

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-2,1).

Crossrefs

Cf. A105495.

Programs

Maple

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

Mathematica

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*)

PARI

Vec((1 + x) / (1 - 4*x + 2*x^2 - x^3) + O(x^30)) \\ Colin Barker, Mar 19 2019

Formula

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

a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) for n>2. - Colin Barker, Mar 19 2019