A119306 Expansion of (1-4*x)/(1-x*(1-x)^3).

1, -3, -6, 6, 14, -19, -37, 56, 96, -164, -247, 477, 630, -1378, -1590, 3957, 3963, -11300, -9728, 32104, 23425, -90771, -55006, 255478, 124758, -715923, -268757, 1997808, 531552, -5552220, -884695, 15368813, 834686, -42373618, 2113458, 116369557, -17926357

Offset

0,2

Comments

Row sums of number triangle A119305.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..4534

Index entries for linear recurrences with constant coefficients, signature (1,-3,3,-1).

Formula

G.f.: (1 - 4*x)/(1 - x + 3*x^2 - 3*x^3 + x^4).

a(n) = a(n-1) - 3*a(n-2) + 3*a(n-3) - a(n-4).

a(n) = Sum_{k=0..n} (C(3*k,n-k) + 4*C(3*k,n-k-1))*(-1)^(n-k).

Mathematica

CoefficientList[Series[(1 - 4 x)/(1 - x (1 - x)^3), {x, 0, 36}], x] (* or *) LinearRecurrence[{1, -3, 3, -1}, {1, -3, -6, 6}, 37] (* or *) Table[Sum[(Binomial[3 k, n - k] + 4 Binomial[3 k, n - k - 1]) (-1)^(n - k), {k, 0, n}], {n, 0, 36}] (* Indranil Ghosh, Feb 27 2017 *)

Prog

(PARI) a(n) = sum(k=0, n, (binomial(3*k, n-k)+4*binomial(3*k, n-k-1))*(-1)^(n-k)); \\ Indranil Ghosh, Feb 27 2017

Crossrefs

Sequence in context: A202931 A240250 A239424 * A107972 A238775 A269525

Adjacent sequences: A119303 A119304 A119305 * A119307 A119308 A119309

Keyword

sign,easy

Author

Paul Barry, May 13 2006

Status

approved