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A249736
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Triangular numbers modulo 30.
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0
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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
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OFFSET
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0,3
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COMMENTS
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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}).
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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G.f. = x + 3*x^2 + 6*x^3 + 10*x^4 + 15*x^5 + 21*x^6 + 28*x^7 + 6*x^8 + ...
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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