OFFSET
0,3
COMMENTS
The sequence is periodic with period 60.
Inside the cycle, the left-hand half is mirror of right-hand half:
{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(
{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}).
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).
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
EXAMPLE
G.f. = x + 3*x^2 + 6*x^3 + 10*x^4 + 15*x^5 + 21*x^6 + 28*x^7 + 6*x^8 + ...
PROG
(PARI) a(n) = n*(n+1)/2 % 30; \\ Michel Marcus, Nov 04 2014
(Magma) [(n*(n+1) div 2) mod (30): n in [0.. 75]]; // Vincenzo Librandi, Nov 05 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Nov 04 2014
STATUS
approved