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A289914 Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 7/5. 2
1, 3, 5, 9, 18, 35, 66, 124, 234, 441, 830, 1563, 2944, 5544, 10440, 19661, 37026, 69727, 131310, 247284, 465686, 876981, 1651534, 3110175, 5857092, 11030096, 20771916, 39117745, 73666674, 138729339, 261255578, 491997420, 926531266, 1744846929, 3285901854 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Conjecture: the sequence is strictly increasing.
LINKS
FORMULA
G.f.: 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 7/5.
From Colin Barker, Jul 19 2017: (Start)
G.f.: (1+x)^2*(1-x+x^2-x^3+x^4) / (1-2*x+x^2-2*x^3+x^4).
a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) for n>3.
(End)
MATHEMATICA
z = 2000; r = 7/5;
u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
x]; (* A289914 *)
v = N[u[[z]]/u[[z - 1]], 200]
RealDigits[v, 10][[1]] (* A289915 *)
PROG
(PARI) Vec((1+x)^2*(1-x+x^2-x^3+x^4) / (1-2*x+x^2-2*x^3+x^4) + O(x^50)) \\ Colin Barker, Jul 20 2017
CROSSREFS
Cf. A078140 (includes guide to related sequences), A289915.
Sequence in context: A120941 A108227 A289912 * A251704 A288230 A289262
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 18 2017
STATUS
approved

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Last modified April 20 16:11 EDT 2024. Contains 371844 sequences. (Running on oeis4.)