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A100213 G.f. x* (4-7*x+2*x^2-8*x^4+16*x^5-16*x^6) / ((2*x-1) * (2*x^2-1) * (2*x^2-2*x+1) * (2*x^2+1)). 3
4, 9, 14, 18, 32, 64, 128, 256, 544, 1104, 2144, 4128, 8192, 16384, 32768, 65536, 131584, 263424, 525824, 1049088, 2097152, 4194304, 8388608, 16777216, 33562624, 67129344, 134242304, 268443648, 536870912, 1073741824, 2147483648, 4294967296, 8590065664 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence can be created applying the pos operator (which sums over the positive coefficients)

to the n-th power of the Floretion element (.5 'j + .5 'k + .5 j' + .5 k' + 1 'ii' + 1 e).

LINKS

Table of n, a(n) for n=1..33.

C. Dement, Floretion Online Multiplier.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, 4, -16, 24, -16).

FORMULA

a(n) + A100212(n) = A100215(n) = ((-1)^n)*A009116(n+3) + A100216 + A038503(n+1).

Equation above in Floretian Algebra operator speak: (pos) + (neg) = (ves) = (jes) + (les) + (tes)

a(n-1) = A000079(n+1) + (5*A077957(n)+6*A077957(n-1))/4 + A009545(n)/2 + A009545(n+1) + A077966(n-1) - A077966(n)/4. - R. J. Mathar, May 07 2008

EXAMPLE

a(5) = 32 because (.5 'j + .5 'k + .5 j' + .5 k' + 1 'ii' + 1 e)^5 = - 2 'j - 2 'k - 2 j' - 2 k' + 6 'ii' + 10 'jj' + 10 'kk' + 6 e,

and the sum of all positive coefficients is 6+10+10+6 = 32.

MATHEMATICA

Rest[CoefficientList[Series[x (4-7x+2x^2-8x^4+16x^5-16x^6)/((2x-1)(2x^2-1)(2x^2-2x+1)(2x^2+1)), {x, 0, 40}], x]] (* or *) LinearRecurrence[{4, -6, 4, 4, -16, 24, -16}, {4, 9, 14, 18, 32, 64, 128}, 40] (* Harvey P. Dale, Aug 23 2015 *)

CROSSREFS

Cf. A100212, A100215, A100216, A009116, A038503.

Sequence in context: A172329 A182778 A100215 * A043365 A023738 A070799

Adjacent sequences:  A100210 A100211 A100212 * A100214 A100215 A100216

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Nov 11 2004

EXTENSIONS

Replaced definition with generating function, changed offset to 1. - R. J. Mathar, Mar 12 2010

STATUS

approved

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Last modified July 26 02:08 EDT 2017. Contains 289798 sequences.