This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105333 #13 Apr 18 2025 14:33:11 %S A105333 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, %T A105333 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, %U A105333 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 %N A105333 a(n) = n*(n+1)/2 mod 16. %C A105333 Triangular numbers mod 16. - _Harvey P. Dale_, Oct 12 2012 %C A105333 Periodic with period length 32. - _Ray Chandler_, Apr 18 2025 %H A105333 <a href="/index/Rec#order_31">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). %F A105333 From _Chai Wah Wu_, Apr 17 2025: (Start) %F A105333 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. %F A105333 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) %t A105333 Mod[#,16]&/@Accumulate[Range[0,90]] (* _Harvey P. Dale_, Oct 12 2012 *) %o A105333 (Python) %o A105333 def A105333(n): return (n*(n+1)>>1)&15 # _Chai Wah Wu_, Apr 17 2025 %Y A105333 Cf. A000217. %Y A105333 See A105198 for further information. %K A105333 nonn %O A105333 0,3 %A A105333 _Oscar Takeshita_, May 01 2005