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A318777 Coefficients in expansion of 1/(1 - x - 2*x^5). 2
1, 1, 1, 1, 1, 3, 5, 7, 9, 11, 17, 27, 41, 59, 81, 115, 169, 251, 369, 531, 761, 1099, 1601, 2339, 3401, 4923, 7121, 10323, 15001, 21803, 31649, 45891, 66537, 96539, 140145, 203443, 295225, 428299, 621377, 901667, 1308553, 1899003, 2755601, 3998355, 5801689, 8418795 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

The coefficients in the expansion of 1/(1 - x - 2*x^5) are given by the sequence generated by the row sums in triangle A318775.

Coefficients in expansion of 1/(1 - x - 2*x^5) are given by the sum of numbers along "fourth Layer" skew diagonals pointing top-right in triangle A013609 ((1+2x)^n) and by the sum of numbers along "fourth Layer" skew diagonals pointing top-left in triangle A038207 ((2+x)^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

Table of n, a(n) for n=0..45.

Zagros Lalo, Fourth layer skew diagonals in center-justified triangle of coefficients in expansion of (1 + 2x)^n.

Zagros Lalo, Fourth layer skew diagonals in center-justified triangle of coefficients in expansion of (2 + x)^n.

FORMULA

a(0)=1, a(n) = a(n-1) + 2 * a(n-5) for n = 0,1...; a(n)=0 for n < 0.

MAPLE

seq(coeff(series((1-x-2*x^5)^(-1), x, n+1), x, n), n = 0 .. 50); # Muniru A Asiru, Sep 26 2018

MATHEMATICA

a[0] = 1; a[n_] := a[n] = If[n < 0, 0, a[n - 1] + 2 * a[n - 5]]; Table[a[n], {n, 0, 45}] // Flatten

LinearRecurrence[{1, 0, 0, 0, 2}, {1, 1, 1, 1, 1}, 46]

CoefficientList[Series[1/(1 - x - 2 x^5), {x, 0, 45}], x]

PROG

(GAP) a:=[1, 1, 1, 1, 1, 3];; for n in [7..50] do a[n]:=a[n-1]+2*a[n-5]; od; a; # Muniru A Asiru, Sep 26 2018

CROSSREFS

Cf. A318775, A318776.

Cf. A013609, A038207.

Essentially a duplicate of A143447.

Sequence in context: A064076 A050842 A143447 * A152484 A071643 A039578

Adjacent sequences:  A318774 A318775 A318776 * A318778 A318779 A318780

KEYWORD

nonn,easy

AUTHOR

Zagros Lalo, Sep 25 2018

STATUS

approved

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Last modified June 20 17:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)