A318777 Coefficients in expansion of 1/(1 - x - 2*x^5).
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
Offset: 0
References
- Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3.
Links
- 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.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2).
Programs
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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
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Maple
seq(coeff(series((1-x-2*x^5)^(-1),x,n+1), x, n), n = 0 .. 50); # Muniru A Asiru, Sep 26 2018
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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]
Formula
a(0)=1, a(n) = a(n-1) + 2 * a(n-5) for n = 0,1...; a(n)=0 for n < 0.
G.f.: -1/(2*x^5 + x - 1). - Chai Wah Wu, Aug 03 2020
Comments