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A318774 Coefficients in expansion of 1/(1 - x - 3*x^4). 2
1, 1, 1, 1, 4, 7, 10, 13, 25, 46, 76, 115, 190, 328, 556, 901, 1471, 2455, 4123, 6826, 11239, 18604, 30973, 51451, 85168, 140980, 233899, 388252, 643756, 1066696, 1768393, 2933149, 4864417, 8064505, 13369684, 22169131, 36762382, 60955897, 101064949, 167572342, 277859488, 460727179, 763922026, 1266639052 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The coefficients in the expansion of 1/(1 - x - 3*x^4) are given by the sequence generated by the row sums in triangle A318772.

Coefficients in expansion of 1/(1 - x - 3*x^4) are given by the sum of numbers along "third Layer" skew diagonals pointing top-right in triangle A013610 ((1+3x)^n) and by the sum of numbers along "third Layer" skew diagonals pointing top-left in triangle A027465 ((3+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..43.

Zagros Lalo, Third layer skew diagonals in center-justified triangle of coefficients in expansion of (1 + 3 x)^n

Zagros Lalo, Third layer skew diagonals in center-justified triangle of coefficients in expansion of (3 + x)^n

FORMULA

a(0)=1, a(n) = a(n-1) + 3*a(n-4) for n >= 0; a(n)=0 for n < 0.

MATHEMATICA

CoefficientList[Series[1/(1 - x - 3 x^4), {x, 0, 40}], x].

a[0] = 1; a[n_] := a[n] = If[n < 0, 0, a[n - 1] + 3 * a[n - 4]]; Table[a[n], {n, 0, 40}] // Flatten.

LinearRecurrence[{1, 0, 0, 3}, {1, 1, 1, 1}, 41].

CROSSREFS

Cf. A013610, A027465.

Cf. A318772, A318773.

Essentially a duplicate of A143454.

Sequence in context: A091290 A119256 A143454 * A065810 A123837 A125620

Adjacent sequences:  A318771 A318772 A318773 * A318775 A318776 A318777

KEYWORD

nonn,easy

AUTHOR

Zagros Lalo, Sep 04 2018

STATUS

approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)