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A317509 Coefficients in Expansion of 1/(1 + x - 2*x^5). 1
1, -1, 1, -1, 1, 1, -3, 5, -7, 9, -7, 1, 9, -23, 41, -55, 57, -39, -7, 89, -199, 313, -391, 377, -199, -199, 825, -1607, 2361, -2759, 2361, -711, -2503, 7225, -12743, 17465, -18887, 13881, 569, -26055, 60985, -98759, 126521 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
Coefficients in expansion of 1/(1 + x - 2*x^5) are given by the sum of numbers along "fourth Layer" skew diagonals pointing top-left in triangle A065109 ((2-x)^n) and by the sum of numbers along "fourth Layer" skew diagonals pointing top-right in triangle A303872 ((-1+2x)^n), see links.
REFERENCES
Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3.
LINKS
FORMULA
a(0)=1, a(n) = -1 * a(n-1) + 2 * a(n-5) for n >= 0; a(n)=0 for n < 0.
MATHEMATICA
CoefficientList[Series[1/(1 + x - 2 x^5), {x, 0, 42}], x].
a[0] = 1; a[n_] := a[n] = If[n < 0, 0, - a[n - 1] + 2 * a[n - 5]]; Table[a[n], {n, 0, 42}] // Flatten.
LinearRecurrence[{-1, 0, 0, 0, 2}, {1, -1, 1, -1, 1}, 43].
PROG
(PARI) x='x+O('x^99); Vec(1/(1+x-2*x^5)) \\ Altug Alkan, Sep 04 2018
CROSSREFS
Sequence in context: A122641 A140977 A161821 * A139083 A252002 A139081
KEYWORD
sign,easy
AUTHOR
Shara Lalo, Sep 04 2018
STATUS
approved

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Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)