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A105334 a(n) = n*(n+1)/2 mod 32.

%I A105334 #12 Apr 18 2025 14:34:35
%S A105334 0,1,3,6,10,15,21,28,4,13,23,2,14,27,9,24,8,25,11,30,18,7,29,20,12,5,
%T A105334 31,26,22,19,17,16,16,17,19,22,26,31,5,12,20,29,7,18,30,11,25,8,24,9,
%U A105334 27,14,2,23,13,4,28,21,15,10,6,3,1,0,0,1,3,6,10,15,21,28,4,13,23,2,14,27,9,24
%N A105334 a(n) = n*(n+1)/2 mod 32.
%C A105334 Periodic with period length 64. - _Ray Chandler_, Apr 18 2025
%H A105334 <a href="/index/Rec#order_63">Index entries for linear recurrences with constant coefficients</a>, 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,-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,-1,1).
%F A105334 From _Chai Wah Wu_, Apr 17 2025: (Start)
%F A105334 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) - a(n-32) + a(n-33) - a(n-34) + a(n-35) - a(n-36) + a(n-37) - a(n-38) + a(n-39) - a(n-40) + a(n-41) - a(n-42) + a(n-43) - a(n-44) + a(n-45) - a(n-46) + a(n-47) - a(n-48) + a(n-49) - a(n-50) + a(n-51) - a(n-52) + a(n-53) - a(n-54) + a(n-55) - a(n-56) + a(n-57) - a(n-58) + a(n-59) - a(n-60) + a(n-61) - a(n-62) + a(n-63) for n > 62.
%F A105334 G.f.: x*(-x^60 - 2*x^59 - 4*x^58 - 6*x^57 - 9*x^56 - 12*x^55 - 16*x^54 + 12*x^53 - 25*x^52 + 2*x^51 - 4*x^50 - 10*x^49 - 17*x^48 + 8*x^47 - 32*x^46 + 24*x^45 - 49*x^44 + 38*x^43 - 68*x^42 + 50*x^41 - 57*x^40 + 28*x^39 - 48*x^38 + 36*x^37 - 41*x^36 + 10*x^35 - 36*x^34 + 14*x^33 - 33*x^32 + 16*x^31 - 32*x^30 + 16*x^29 - 33*x^28 + 14*x^27 - 36*x^26 + 10*x^25 - 41*x^24 + 36*x^23 - 48*x^22 + 28*x^21 - 57*x^20 + 50*x^19 - 68*x^18 + 38*x^17 - 49*x^16 + 24*x^15 - 32*x^14 + 8*x^13 - 17*x^12 - 10*x^11 - 4*x^10 + 2*x^9 - 25*x^8 + 12*x^7 - 16*x^6 - 12*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)*(x^32 + 1)). (End)
%t A105334 Mod[Accumulate[Range[0,80]],32] (* _Harvey P. Dale_, Sep 01 2017 *)
%o A105334 (Python)
%o A105334 def A105334(n): return (n*(n+1)>>1)&31 # _Chai Wah Wu_, Apr 17 2025
%Y A105334 Cf. A000217.
%Y A105334 See A105198 for further information.
%K A105334 nonn
%O A105334 0,3
%A A105334 _Oscar Takeshita_, May 01 2005