A249736 Triangular numbers modulo 30.
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, 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, 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
Offset: 0
Examples
G.f. = x + 3*x^2 + 6*x^3 + 10*x^4 + 15*x^5 + 21*x^6 + 28*x^7 + 6*x^8 + ...
Links
- Index entries for linear recurrences with constant coefficients, 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).
Programs
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Magma
[(n*(n+1) div 2) mod (30): n in [0.. 75]]; // Vincenzo Librandi, Nov 05 2014
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PARI
a(n) = n*(n+1)/2 % 30; \\ Michel Marcus, Nov 04 2014
Formula
a(n) = A000217(n) mod 30.
a(n) = a(-1-n) = a(n+60) for all n in Z. - Michael Somos, Nov 06 2014
0 = a(n) - a(n+15) + a(n+30) - a(n+45) for all n in Z. - Michael Somos, Nov 06 2014
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
Comments