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 A176346 A dual remainder symmetrical triangle sequence T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)), read by rows. 2
 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 2, 3, 3, 2, 1, 1, 3, 4, 7, 4, 3, 1, 1, 2, 5, 4, 4, 5, 2, 1, 1, 3, 3, 5, 9, 5, 3, 3, 1, 1, 2, 4, 6, 5, 5, 6, 4, 2, 1, 1, 3, 5, 7, 6, 11, 6, 7, 5, 3, 1, 1, 2, 3, 4, 7, 6, 6, 7, 4, 3, 2, 1, 1, 3, 4, 5, 8, 7, 13, 7, 8, 5, 4, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This sequence comes from computability functions. Row sums are : {1, 2, 5, 6, 13, 12, 23, 24, 33, 36, 55,...}. REFERENCES N. J. Cutland, "Computability, An introduction to recursive function theory", Cambridge University Press, London, 1980, page 37. Martin Davis, "Computability and Unsolvability", Dover Press, New York, page 43. LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)). EXAMPLE Triangle begins as: 1; 1, 1; 1, 3, 1; 1, 2, 2, 1; 1, 3, 5, 3, 1; 1, 2, 3, 3, 2, 1; 1, 3, 4, 7, 4, 3, 1; 1, 2, 5, 4, 4, 5, 2, 1; 1, 3, 3, 5, 9, 5, 3, 3, 1; 1, 2, 4, 6, 5, 5, 6, 4, 2, 1; 1, 3, 5, 7, 6, 11, 6, 7, 5, 3, 1; MATHEMATICA T[n_, m_]:= 3 +2*n -(m+1)*Floor[(n+1)/(m+1)] -(n-m+1)*Floor[(n+1)/(n-m+1 )]; Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 26 2019 *) PROG (PARI) {T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)* floor((n+1)/(n-m+1))}; \\ G. C. Greubel, Apr 26 2019 (Magma) [[1 + 2*(n+1) - (m+1)*Floor((n+1)/(m+1)) - (n-m+1)*Floor((n+1)/( n-m+1)): m in [0..n]]: n in [0..12]]; // G. C. Greubel, Apr 26 2019 (Sage) [[1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)) for m in (0..n)] for n in (0..12)] # G. C. Greubel, Apr 26 2019 CROSSREFS Cf. A176298. Sequence in context: A356400 A153066 A126209 * A338878 A073166 A050169 Adjacent sequences: A176343 A176344 A176345 * A176347 A176348 A176349 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Apr 15 2010 EXTENSIONS Edited by G. C. Greubel, Apr 26 2019 STATUS approved

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Last modified June 9 17:32 EDT 2023. Contains 363183 sequences. (Running on oeis4.)