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A033453
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"INVERT" transform of squares A000290.
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272
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MAPLE
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read transforms; [seq(n^2, n=1..50)]; INVERT(%);
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MATHEMATICA
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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*)
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PROG
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(PARI) Vec((1 + x) / (1 - 4*x + 2*x^2 - x^3) + O(x^30)) \\ Colin Barker, Mar 19 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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