

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 topleft in triangle A065109 ((2x)^n) and by the sum of numbers along "fourth Layer" skew diagonals pointing topright in triangle A303872 ((1+2x)^n), see links.


REFERENCES

Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 9781999591403.


LINKS



FORMULA

a(0)=1, a(n) = 1 * a(n1) + 2 * a(n5) 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+x2*x^5)) \\ Altug Alkan, Sep 04 2018


CROSSREFS



KEYWORD

sign,easy


AUTHOR



STATUS

approved



