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A143372 A new 4 symbol polynomial of the Weaver telegraphic type: dot:x^2; dash:x^4; Letter space:2 + x^2 + x^3; Word space:1 + x- x^3 - x^4 + x^6; p(y)=-5 - 3 y - 7 y^2 - 3 y^3 + 2 y^4 + 3 y^5 + 2 y^6 + 2 y^7 - 3 y^8 - y^9 - y^10 - 2 y^11 + y^12 + y^13. 0
1, -1, 3, -4, 10, -13, 27, -38, 70, -99, 173, -242, 400, -548, 869, -1136, 1718, -2088, 2936, -3033, 3615, -1763, -513, 10082, -24172, 58958, -111749, 220258, -385285, 693194, -1157154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37 - 38

LINKS

Table of n, a(n) for n=1..31.

FORMULA

p(y)=-5 - 3 y - 7 y^2 - 3 y^3 + 2 y^4 + 3 y^5 + 2 y^6 + 2 y^7 - 3 y^8 - y^9 - y^10 - 2 y^11 + y^12 + y^13; a(n)=coefficient_expansion(x^13*p(1/x))

EXAMPLE

Weaver determinant:

Expand[FullSimplify[ExpandAll[y^4 *(2 + y^2 + y^3)(1 +y - y^3 - y^4 + y^6)*Det[{{-1, ((1/y^4 + 1/y^2))},

{1/((1 + y - y^3 - y^4 +y^6)) + 1/((2 + y^2 + y^3), 1/y^2 + 1/y^4 - 1}}]]]].

MATHEMATICA

p[y_] = -5 - 3 y - 7 y^2 - 3 y^3 + 2 y^4 + 3 y^5 + 2 y^6 + 2 y^7 - 3 y^8 - y^9 - y^10 - 2 y^11 + y^12 + y^13; q[x_] = ExpandAll[x^13*p[1/x]]; a = Table[SeriesCoefficient[Series[1/q[x], {x, 0, 30}], n], {n, 0, 30}]

CROSSREFS

Cf. A122762.

Sequence in context: A257494 A302347 A092119 * A035594 A167273 A096380

Adjacent sequences:  A143369 A143370 A143371 * A143373 A143374 A143375

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 22 2008

STATUS

approved

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Last modified December 11 15:03 EST 2018. Contains 318049 sequences. (Running on oeis4.)