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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 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 = 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.)