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 A108872 Sums of ordinal references for a triangular table read by columns, top to bottom. 4
 2, 3, 4, 4, 5, 6, 5, 6, 7, 8, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 12, 8, 9, 10, 11, 12, 13, 14, 9, 10, 11, 12, 13, 14, 15, 16, 10, 11, 12, 13, 14, 15, 16, 17, 18, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The ordinal references (i,j) for a triangular table are arranged as follows: (1,1) (2,1) (3,1) ..... (2,2) (3,2) ........... (3,3) The sequence comprises the sum of each reference in each column, read top to bottom. A similar sequence is A003057, which consists of the sums of the ordinal references for an array read by antidiagonals. Subtriangle of triangle in A051162. - Philippe Deléham, Mar 26 2013 First 9 rows coincide with triangle A248110; T(n,k) = A002260(n,k) + n; T(2*n-1,n) = A016789(n-1). - Reinhard Zumkeller, Oct 01 2014 LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened NRICH discussion thread, Floor Function Identity. [Via Wayback Machine] FORMULA a(n) = a(i, j) = i + j a(n) = A002024(n) + A002260(n) = floor(1/2 + sqrt(2n)) + n - (m(m+1)/2) + 1, where m = floor((sqrt(8n+1) - 1) / 2 ). The floor function may be computed directly by using the expression floor(x) = x + (arctan(cot(Pi*x)) / Pi) - 1/2 (equation from nrich.maths.org, see links). sum(k=0..n, T(n,k)) = A005449(n+1). - Philippe Deléham, Mar 26 2013 EXAMPLE a(1) = (1,1) = 1 + 1 = 2 a(2) = (2,1) = 2 + 1 = 3 a(3) = (2,2) = 2 + 2 = 4 a(4) = (3,1) = 3 + 1 = 4, etc. Triangle begins: 2 3, 4 4, 5, 6 5, 6, 7, 8 6, 7, 8, 9, 10 7, 8, 9, 10, 11, 12 8, 9, 10, 11, 12, 13, 14 9, 10, 11, 12, 13, 14, 15, 16 ... - Philippe Deléham, Mar 26 2013 MATHEMATICA Flatten[ Table[i + j, {j, 1, 12}, {i, 1, j}]] (* Jean-François Alcover, Oct 07 2011 *) PROG (Haskell) a108872 n k = a108872_tabl !! (n-1) !! (k-1) a108872_row n = a108872_tabl !! (n-1) a108872_tabl = map (\x -> [x + 1 .. 2 * x]) [1..] -- Reinhard Zumkeller, Oct 01 2014 CROSSREFS Cf. A003057. Cf. A002024, A002260. Cf. A005408, A005843. Cf. A016789 (central terms), A248110. Sequence in context: A101504 A125568 A248110 * A147847 A370386 A335572 Adjacent sequences: A108869 A108870 A108871 * A108873 A108874 A108875 KEYWORD easy,nonn,tabl AUTHOR Andrew S. Plewe, Jul 13 2005 EXTENSIONS Offset changed by Reinhard Zumkeller, Oct 01 2014 STATUS approved

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Last modified July 20 15:46 EDT 2024. Contains 374459 sequences. (Running on oeis4.)