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

0,3

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

Table of n, a(n) for n=0..84.

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

Cf. A000217, A249622.

Sequence in context: A171971 A184009 A105334 * A371473 A130486 A054636

Adjacent sequences: A249733 A249734 A249735 * A249737 A249738 A249739

Keyword

nonn,easy

Author

Zak Seidov, Nov 04 2014

Status

approved