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A279816
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Digital roots of tetrahedral numbers (A000292).
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0
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0, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9
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OFFSET
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0,3
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COMMENTS
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Period 27: repeat [1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9] for n >= 1.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1).
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FORMULA
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G.f.: x*(1 + 4*x + x^2 + 2*x^3 + 8*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 3*x^8 + 4*x^9 + 7*x^10 + 4*x^11 + 5*x^12 + 2*x^13 + 5*x^14 + 6*x^15 + 6*x^16 + 6*x^17 + 7*x^18 + x^19 + 7*x^20 + 8*x^21 + 5*x^22 + 8*x^23 + 9*x^24 + 9*x^25 + 9*x^26)/(1 - x^27).
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EXAMPLE
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a(6) = 2 because the 6th tetrahedral number is 56, 5 + 6 = 11 -> 1 + 1 = 2.
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MATHEMATICA
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Join[{0}, Table[n (n + 1) (n + 2)/6 - 9 Floor[(n - 1) (n^2 + 4 n + 6)/54], {n, 108}]]
Join[{0}, LinearRecurrence[{1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1}, {1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9}, 108]]
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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