A242062 Expansion of x * (1 - x^12) / ((1 - x^3) * (1 - x^4) * (1 - x^7)) in powers of x.

0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 2, 3, 3, 2, 3, 4, 3, 3, 4, 4, 3, 4, 5, 4, 4, 5, 5, 4, 5, 6, 5, 5, 6, 6, 5, 6, 7, 6, 6, 7, 7, 6, 7, 8, 7, 7, 8, 8, 7, 8, 9, 8, 8, 9, 9, 8, 9, 10, 9, 9, 10, 10, 9, 10, 11, 10, 10, 11, 11, 10, 11, 12, 11, 11, 12

Offset

0,9

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Formula

Euler transform of length 12 sequence [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -1].

G.f.: x * (1 - x + x^3 - x^5 + x^6) / (1 - x - x^7 + x^8).

G.f.: x / (1 - x^3 / (1 - x / (1 + x / (1 - x^5 / (1 - x / (1 + x^2 / (1 - x^2))))))).

a(n) = -a(-n) = a(n-7) + 1 = a(n-1) + a(n-7) - a(n-8) for all n in Z.

0 = 2*a(n) - a(n+1) + a(n+2) - 2*a(n+3) + (a(n+1) - a(n+2))^2 for all n in Z.

a(n+1) - a(n) = A131372(n).

Example

G.f. = x + x^4 + x^5 + x^7 + 2*x^8 + x^9 + x^10 + 2*x^11 + 2*x^12 + x^13 + ...

Maple

a:= n -> [0, 1, 0, 0, 1, 1, 0][n mod 7 + 1] + floor(n/7):
seq(a(n), n=0..20); # Robert Israel, Aug 13 2014

Mathematica

a[ n_] := Quotient[ n+3, 7] + {1, 0, 0, 0, 0, -1, 0}[[Mod[ n, 7, 1]]];
a[ n_] := Sign[n] * SeriesCoefficient[ x * (1 - x^12) / ((1 - x^3) * (1 - x^4) * (1 - x^7)), {x, 0, Abs[n]}];
CoefficientList[Series[x (1 - x + x^3 - x^5 + x^6)/(1 - x - x^7 + x^8), {x, 0, 100}], x] (* Vincenzo Librandi, Aug 14 2014 *)

Prog

(PARI) {a(n) = (n+3)\7 + (n%7==1) - (n%7==6)};
(PARI) {a(n) = sign(n) * polcoeff( x * (1 - x^12) / ((1 - x^3) * (1 - x^4) * (1 - x^7)) + x * O(x^abs(n)), abs(n))};
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 -x+x^3-x^5+x^6)/(1-x-x^7+x^8))); // G. C. Greubel, Aug 05 2018

Crossrefs

Cf. A131372.

Sequence in context: A352578 A278341 A276520 * A025848 A268197 A065382

Adjacent sequences: A242059 A242060 A242061 * A242063 A242064 A242065

Keyword

nonn

Author

Michael Somos, Aug 13 2014

Status

approved