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A104581 Expansion of 1/(1 + x + x^3 + x^4). 0
1, -1, 1, -2, 2, -2, 3, -3, 3, -4, 4, -4, 5, -5, 5, -6, 6, -6, 7, -7, 7, -8, 8, -8, 9, -9, 9, -10, 10, -10, 11, -11, 11, -12, 12, -12, 13, -13, 13, -14, 14, -14, 15, -15, 15, -16, 16, -16, 17, -17, 17, -18, 18, -18, 19, -19, 19, -20, 20, -20, 21, -21, 21, -22, 22, -22, 23, -23, 23, -24, 24, -24, 25, -25, 25, -26, 26, -26 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Diagonal sums of Riordan array (1/(1+x+x^2+x^3+x^4),x/(1+x+x^2+x^3+x^4)). Convolution of (n+1)(-1)^n and A010892.

LINKS

Table of n, a(n) for n=0..77.

Index entries for linear recurrences with constant coefficients, signature (-1,0,-1,-1).

FORMULA

a(n) = floor((n+3)/3)(-1)^n; a(n) = Sum_{k=0..n} ((n-k+1)(-1)^(n-k)*2sin(Pi*k/3 + Pi/3)/sqrt(3)).

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

MATHEMATICA

CoefficientList[ Series[1/(1 + x + x^3 + x^4), {x, 0, 80}], x] (* Robert G. Wilson v, Mar 24 2005 *)

LinearRecurrence[{-1, 0, -1, -1}, {1, -1, 1, -2}, 90] (* Harvey P. Dale, Jan 18 2019 *)

CROSSREFS

Cf. A008620.

Sequence in context: A086161 A002264 A008620 * A261916 A113675 A020912

Adjacent sequences:  A104578 A104579 A104580 * A104582 A104583 A104584

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 16 2005

STATUS

approved

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Last modified November 15 06:11 EST 2019. Contains 329144 sequences. (Running on oeis4.)