A135687 a(n) = a(n-1) - A004001(n)*a(n-2), a(1) = 1, a(2) = 1.
1, 1, -1, -3, 0, 12, 12, -36, -96, 120, 792, -48, -6384, -6000, 45072, 93072, -312576, -1243296, 2195040, 17114592, -9225888, -231715584, -102553152, 3141465024, 4679762304, -42442213056, -112638647616, 566436761280, 2368655123136, -6694333057344, -44592815027520
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..500
Programs
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Mathematica
HC[n_]:= HC[n]= If[n<3, Fibonacci[n], HC[HC[n-1]] +HC[n -HC[n-1]]]; (*A004001*) a[n_]:= a[n]= If[n<3, 1, a[n-1] - HC[n]*a[n-2]]; Table[a[n], {n, 40}]
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Sage
@cached_function def HC(n): # HC = A004001 if (n<3): return fibonacci(n) else: return HC(HC(n-1)) +HC(n -HC(n-1)) @CachedFunction def a(n): # A135688 if (n<3): return 1 else: return a(n-1) - HC(n)*a(n-2) [a(n) for n in (1..40)] # G. C. Greubel, Nov 25 2021
Formula
a(n) = a(n-1) - A004001(n)*a(n-2), with a(1) = a(2) = 1.