A345009 - OEIS

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A345009

a(0) = 1; a(5*n) = a(n) - a(n-1), a(5*n+1) = a(5*n+2) = a(5*n+3) = a(5*n+4) = a(n).

1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, 1

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OFFSET

LINKS

Table of n, a(n) for n=0..105.

FORMULA

G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4 - x^5) * A(x^5).

G.f.: Product_{k>=0} (1 + x^(5^k) + x^(2*5^k) + x^(3*5^k) + x^(4*5^k) - x^(5^(k+1))).

MATHEMATICA

a[0] = 1; a[n_] := Switch[Mod[n, 5], 0, a[n/5] - a[(n - 5)/5], 1, a[(n - 1)/5], 2, a[(n - 2)/5], 3, a[(n - 3)/5], 4, a[(n - 4)/5]]; Table[a[n], {n, 0, 105}]

nmax = 105; A[_] = 1; Do[A[x_] = (1 + x + x^2 + x^3 + x^4 - x^5) A[x^5] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

nmax = 105; CoefficientList[Series[Product[(1 + x^(5^k) + x^(2 5^k) + x^(3 5^k) + x^(4 5^k) - x^(5^(k + 1))), {k, 0, Floor[Log[5, nmax]] + 1}], {x, 0, nmax}], x]

CROSSREFS

Cf. A005590, A277873, A309048, A345008.

Sequence in context: A236862 A163812 A163818 * A071040 A336834 A356173

Adjacent sequences: A345006 A345007 A345008 * A345010 A345011 A345012

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 05 2021

STATUS

approved