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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 (list; graph; refs; listen; history; text; internal format)
 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 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-2,1). 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: A111567 A121050 A029869 * A284840 A301749 A222373 Adjacent sequences:  A033450 A033451 A033452 * A033454 A033455 A033456 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 14 00:10 EDT 2019. Contains 327990 sequences. (Running on oeis4.)