%I #19 Sep 08 2022 08:46:10
%S 0,1,3,6,10,15,21,28,6,15,25,6,18,1,15,0,16,3,21,10,0,21,13,6,0,25,21,
%T 18,16,15,15,16,18,21,25,0,6,13,21,0,10,21,3,16,0,15,1,18,6,25,15,6,
%U 28,21,15,10,6,3,1,0,0,1,3,6,10,15,21,28,6,15,25,6,18,1,15,0,16,3,21,10,0,21,13,6,0
%N Triangular numbers modulo 30.
%C The sequence is periodic with period 60.
%C Inside the cycle, the left-hand half is mirror of right-hand half:
%C {0, 1, 3, 6, 10, 15, 21, 28, 6, 15, 25, 6, 18, 1, 15, 0, 16, 3, 21, 10, 0, 21, 13, 6, 0, 25, 21, 18, 16, 15} = reverse(
%C {15, 16, 18, 21, 25, 0, 6, 13, 21, 0, 10, 21, 3, 16, 0, 15, 1, 18, 6, 25, 15, 6, 28, 21, 15, 10, 6, 3, 1, 0}).
%H <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F a(n) = A000217(n) mod 30.
%F a(n) = a(-1-n) = a(n+60) for all n in Z. - _Michael Somos_, Nov 06 2014
%F 0 = a(n) - a(n+15) + a(n+30) - a(n+45) for all n in Z. - _Michael Somos_, Nov 06 2014
%F b(n) = a(n) - a(n+2) - a(n+4) - a(n+6) for all n in Z where b(n) is either -22 or 8 depending on n mod 60. - _Michael Somos_, Nov 06 2014
%e G.f. = x + 3*x^2 + 6*x^3 + 10*x^4 + 15*x^5 + 21*x^6 + 28*x^7 + 6*x^8 + ...
%o (PARI) a(n) = n*(n+1)/2 % 30; \\ _Michel Marcus_, Nov 04 2014
%o (Magma) [(n*(n+1) div 2) mod (30): n in [0.. 75]]; // _Vincenzo Librandi_, Nov 05 2014
%Y Cf. A000217, A249622.
%K nonn,easy
%O 0,3
%A _Zak Seidov_, Nov 04 2014