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 A289912 Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = sqrt(2). 2

%I #5 Jul 19 2017 20:15:51

%S 1,3,5,9,18,35,66,124,234,441,829,1557,2925,5496,10325,19394,36429,

%T 68428,128532,241425,453475,851775,1599910,3005145,5644626,10602419,

%U 19914742,37406262,70260933,131972522,247886635,465610427,874565375,1642713630,3085541851

%N Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = sqrt(2).

%C Conjecture: the sequence is strictly increasing.

%F G.f.: 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = sqrt(2).

%t z = 100; r = Sqrt[2];

%t u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],

%t x]; (* A289912 *)

%t v = N[u[[z]]/u[[z - 1]], 200]

%t d = RealDigits[v, 10][[1]] (* A289913 *)

%Y Cf. A078140 (includes guide to related sequences), A289913.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jul 18 2017

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Last modified May 21 02:29 EDT 2024. Contains 372720 sequences. (Running on oeis4.)