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A245320 Coefficients of "optimum L" polynomials L_n(ω^2) ordered by increasing powers. 0
0, 0, 1, 0, 0, 1, 0, 1, -3, 3, 0, 0, 3, -8, 6, 0, 1, -8, 28, -40, 20, 0, 0, 6, -40, 105, -120, 50, 0, 1, -15, 105, -355, 615, -525, 175, 0, 0, 10, -120, 615, -1624, 2310, -1680, 490, 0, 1, -24, 276, -1624, 5376, -10416, 11704, -7056, 1764, 0, 0, 15, -280 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Used in the generation of "optimum L" (or Legendre-Papoulis) filters.
REFERENCES
A. Papoulis, ”On Monotonic Response Filters,” Proc. IRE, 47, No. 2, Feb. 1959, 332-333 (correspondence section)
LINKS
A. Papoulis, Optimum Filters with Monotonic Response, Proc. IRE, 46, No. 3, March 1958, pp. 606-609.
EXAMPLE
Triangle begins:
0;
0, 1;
0, 0, 1;
0, 1, -3, 3;
0, 0, 3, -8, 6;
0, 1, -8, 28, -40, 20;
0, 0, 6, -40, 105, -120, 50;
...
So:
L_4(ω^2) = 0 + 0ω^2 + 3ω^4 - 8ω^6 + 6ω^8
L_5(ω^2) = 0 + 1ω^2 - 8ω^4 + 28ω^6 - 40ω^8 + 20ω^10
CROSSREFS
Derived from A100258 and A060818.
Sequence in context: A109247 A021307 A170852 * A330341 A152893 A335682
KEYWORD
sign,tabl
AUTHOR
Jonathan Bright, Jul 17 2014
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)