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A318774 Coefficients in expansion of 1/(1 - x - 3*x^4). 2

%I

%S 1,1,1,1,4,7,10,13,25,46,76,115,190,328,556,901,1471,2455,4123,6826,

%T 11239,18604,30973,51451,85168,140980,233899,388252,643756,1066696,

%U 1768393,2933149,4864417,8064505,13369684,22169131,36762382,60955897,101064949,167572342,277859488,460727179,763922026,1266639052

%N Coefficients in expansion of 1/(1 - x - 3*x^4).

%C 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.

%C 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.

%D Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3.

%H Zagros Lalo, <a href="/A318774/a318774_1.pdf">Third layer skew diagonals in center-justified triangle of coefficients in expansion of (1 + 3 x)^n</a>

%H Zagros Lalo, <a href="/A318774/a318774.pdf">Third layer skew diagonals in center-justified triangle of coefficients in expansion of (3 + x)^n</a>

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

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

%t 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.

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

%Y Cf. A013610, A027465.

%Y Cf. A318772, A318773.

%Y Essentially a duplicate of A143454.

%K nonn,easy

%O 0,5

%A _Zagros Lalo_, Sep 04 2018

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Last modified October 21 06:24 EDT 2019. Contains 328292 sequences. (Running on oeis4.)