A105333 a(n) = n*(n+1)/2 mod 16.
0, 1, 3, 6, 10, 15, 5, 12, 4, 13, 7, 2, 14, 11, 9, 8, 8, 9, 11, 14, 2, 7, 13, 4, 12, 5, 15, 10, 6, 3, 1, 0, 0, 1, 3, 6, 10, 15, 5, 12, 4, 13, 7, 2, 14, 11, 9, 8, 8, 9, 11, 14, 2, 7, 13, 4, 12, 5, 15, 10, 6, 3, 1, 0, 0, 1, 3, 6, 10, 15, 5, 12, 4, 13, 7, 2, 14, 11, 9, 8, 8, 9, 11, 14, 2, 7, 13, 4, 12
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1).
Programs
-
Mathematica
Mod[#,16]&/@Accumulate[Range[0,90]] (* Harvey P. Dale, Oct 12 2012 *)
-
Python
def A105333(n): return (n*(n+1)>>1)&15 # Chai Wah Wu, Apr 17 2025
Formula
From Chai Wah Wu, Apr 17 2025: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) - a(n-14) + a(n-15) - a(n-16) + a(n-17) - a(n-18) + a(n-19) - a(n-20) + a(n-21) - a(n-22) + a(n-23) - a(n-24) + a(n-25) - a(n-26) + a(n-27) - a(n-28) + a(n-29) - a(n-30) + a(n-31) for n > 30.
G.f.: x*(-x^28 - 2*x^27 - 4*x^26 - 6*x^25 - 9*x^24 + 4*x^23 - 16*x^22 + 12*x^21 - 25*x^20 + 18*x^19 - 20*x^18 + 6*x^17 - 17*x^16 + 8*x^15 - 16*x^14 + 8*x^13 - 17*x^12 + 6*x^11 - 20*x^10 + 18*x^9 - 25*x^8 + 12*x^7 - 16*x^6 + 4*x^5 - 9*x^4 - 6*x^3 - 4*x^2 - 2*x - 1)/((x - 1)*(x^2 + 1)*(x^4 + 1)*(x^8 + 1)*(x^16 + 1)). (End)
Comments