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A113066 Expansion of (1+x)^2/((x^2+x+1)*(x^2+3*x+1)). 0
1, -2, 4, -10, 27, -72, 189, -494, 1292, -3382, 8855, -23184, 60697, -158906, 416020, -1089154, 2851443, -7465176, 19544085, -51167078, 133957148, -350704366, 918155951, -2403763488, 6293134513, -16475640050, 43133785636, -112925716858, 295643364939, -774004377960 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform gives signed version of A093040. a(n) + a(n+1) = ((-1)^(n+1))A109961(n+1). a(n) + a(n+1) + a(n+2) = ((-1)^n)A001906(n+2) = ((-1)^n)F(2n+4)

The positive sequence has g.f. (1-x)^2/((1-x+x^2)(1-3x+x^2)) and a(n)=sum{k=0..n, C(n+k+1,n-k)*(1+(-1)^k)/2}. [From Paul Barry, Jul 06 2009]

REFERENCES

C. Dement, Floretion Integer Sequences (work in progress).

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (-4,-5,-4,-1).

FORMULA

a(n) = A049347(n)/2 +(-1)^n*A001906(n+1)/2. [From R. J. Mathar, Nov 10 2009]

PROG

Floretion Algebra Multiplication Program, FAMP Code: 2basei[C*F]; C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki'; F = + .5'i + .5'ii' + .5'ij' + .5'ik'

CROSSREFS

Cf. A113067, A113068, A093040, A109961, A001906.

Sequence in context: A173758 A272603 A272602 * A002459 A216434 A220829

Adjacent sequences:  A113063 A113064 A113065 * A113067 A113068 A113069

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Oct 13 2005

STATUS

approved

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Last modified August 22 10:37 EDT 2017. Contains 290946 sequences.