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A033453
"INVERT" transform of squares A000290.
272
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
0,2
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
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
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*)
PROG
(PARI) Vec((1 + x) / (1 - 4*x + 2*x^2 - x^3) + O(x^30)) \\ Colin Barker, Mar 19 2019
CROSSREFS
Cf. A105495.
Sequence in context: A121050 A029869 A373123 * A284840 A301749 A222373
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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