The On-Line Encyclopedia of Integer Sequences (OEIS)

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A325585

G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * ((1 + 5*x)^n - A(x))^(n+1), where A(0) = 0.
(history; published version)

#12 by Wesley Ivan Hurt at Sat May 11 21:56:40 EDT 2019

STATUS

proposed

approved

#11 by Jean-François Alcover at Sat May 11 13:27:37 EDT 2019

STATUS

editing

proposed

#10 by Jean-François Alcover at Sat May 11 13:27:33 EDT 2019

MATHEMATICA

a[n_] := Module[{A}, A={1}; For[i=1, i <= n, i++, AppendTo[A, 0]; A[[-1]] = Coefficient[Sum[x^m*((1 + 5*x + x*O[x]^Length[A])^m - x*(A.x^Range[0, Length[A]-1]))^(m+1), {m, 0, Length[A]}], x, Length[A]]]; A[[n+1]]];

Table[a[n], {n, 0, 24}] (* Jean-François Alcover, May 11 2019, from PARI *)

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approved

editing

#9 by Paul D. Hanna at Sat May 11 13:04:11 EDT 2019

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editing

approved

#8 by Paul D. Hanna at Sat May 11 13:04:09 EDT 2019

FORMULA

a(2*n) = (-1 (mod 5), a(2*^n+1) = -1 (mod 5), for n >= 0.

STATUS

approved

editing

#7 by Paul D. Hanna at Sat May 11 13:01:56 EDT 2019

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editing

approved

#6 by Paul D. Hanna at Sat May 11 13:01:54 EDT 2019

FORMULA

a(2*n) = 0 1 (mod 5), a(2*n+1) = 4 -1 (mod 5), for n >= 0.

STATUS

approved

editing

#5 by Paul D. Hanna at Sat May 11 12:56:27 EDT 2019

STATUS

editing

approved

#4 by Paul D. Hanna at Sat May 11 12:56:25 EDT 2019

LINKS

Paul D. Hanna, <a href="/A325585/b325585.txt">Table of n, a(n) for n = 1..300</a>

STATUS

approved

editing

#3 by Paul D. Hanna at Sat May 11 12:56:06 EDT 2019

STATUS

editing

approved