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 A279816 Digital roots of tetrahedral numbers (A000292). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS Eric Weisstein's World of Mathematics, Digital Root Eric Weisstein's World of Mathematics, Tetrahedral Number 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). FORMULA 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). a(n) = A010888(A000292(n)). EXAMPLE a(6) = 2 because the 6th tetrahedral number is 56, 5 + 6 = 11 -> 1 + 1 = 2. MATHEMATICA 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]] CROSSREFS Cf. A000292, A004160, A010888, A145389. Sequence in context: A096249 A081454 A133883 * A004160 A128077 A128078 Adjacent sequences:  A279813 A279814 A279815 * A279817 A279818 A279819 KEYWORD nonn,base,easy AUTHOR Ilya Gutkovskiy, Dec 19 2016 STATUS approved

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Last modified March 19 00:15 EDT 2019. Contains 321306 sequences. (Running on oeis4.)