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A276991 a(n) = ((phi; phi)_n - (1-phi; 1-phi)_n)/sqrt(5), where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio. 1
0, -1, 0, -2, 8, -86, 1448, -40608, 1867080, -140055600, 17085644400, -3383043446640, 1085946439923840, -564694233102890880, 475471874409018791040, -648068513405723438730240, 1429638846930684965104992000, -5103811083889432701541321459200 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, q-Pochhammer Symbol, Golden Ratio.
FORMULA
(phi; phi)_n = (A276990(n) + a(n)*sqrt(5))/2.
(1-phi; 1-phi)_n = (A276990(n) - a(n)*sqrt(5))/2.
a(n) ~ c * (-1)^n * phi^(n*(n+1)/2) / sqrt(5), where c = (1/phi)_inf = A276987 = 0.1208019218617061294237231569887920563043992516794...
MATHEMATICA
Round@Table[(QPochhammer[GoldenRatio, GoldenRatio, n] - QPochhammer[1 - GoldenRatio, 1 - GoldenRatio, n])/Sqrt[5], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
CROSSREFS
Sequence in context: A306001 A261730 A052456 * A000532 A333366 A083831
KEYWORD
sign
AUTHOR
STATUS
approved

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Last modified July 12 17:45 EDT 2024. Contains 374251 sequences. (Running on oeis4.)