Every odd Lucas number is a sinh, and every even is a cosh up, counting a delta hyperbolic angle of ln(Phi) = 0.481211825. The angles are integer log base Phi. That brings up interesting properties, sinh(k) + cosh(k+d) = sinh(k+2d). And sum of angle identities yields linear combination of Lucas numbers.
Boy I should have looked earlier six months ago, but I am a bit of a dummy.
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