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 A101037 Triangle read by rows: T(n,1) = T(n,n) = n and for 1
 1, 2, 2, 3, 2, 3, 4, 2, 2, 4, 5, 3, 2, 3, 5, 6, 4, 2, 2, 4, 6, 7, 5, 3, 2, 3, 5, 7, 8, 6, 4, 2, 2, 4, 6, 8, 9, 7, 5, 3, 2, 3, 5, 7, 9, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 11, 9, 7, 5, 3, 2, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 12, 13, 11, 9, 7, 5, 3, 2, 3, 5, 7, 9, 11, 13, 14, 12, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 12, 14 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n>1: sum of n-th row = A007590(n+1). LINKS Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened) FORMULA From Robert Israel, Jan 30 2018: (Start) T(n,k) = n - 2*k + 2 if k < (n+1)/2. T(n,(n+1)/2) = 2 if n>1 is odd. T(n,k) = 2*k - n if k > (n+1)/2. G.f. as triangle: x*y*(x^6*y^3-2*x^5*y^3-2*x^5*y^2+x^4*y^3+3*x^4*y^2+x^4*y-3*x^2*y+1)/((1-x^2*y)*(1-x)^2*(1-x*y)^2)). (End) EXAMPLE Triangle begins:   1;   2, 2;   3, 2, 3;   4, 2, 2, 4;   5, 3, 2, 3, 5;   6, 4, 2, 2, 4, 6;   7, 5, 3, 2, 3, 5, 7;   ... MAPLE T:= proc(n, k) if k < (n+1)/2 then n-2*k+2 elif k=(n+1)/2 then 2 else 2*k-n fi end proc: T(1, 1):= 1: seq(seq(T(n, k), k=1..n), n=1..20); # Robert Israel, Jan 30 2018 MATHEMATICA T[n_, 1] := n; T[n_, n_] := n; T[n_, k_] := T[n, k] = Which[k < (n + 1)/2, n - 2*k + 2, k == (n + 1)/2, 2, True, 2*k - n]; Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 04 2019 *) CROSSREFS Sequence in context: A046773 A175402 A281726 * A002199 A218829 A237715 Adjacent sequences:  A101034 A101035 A101036 * A101038 A101039 A101040 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Nov 27 2004 STATUS approved

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Last modified August 18 00:56 EDT 2019. Contains 326059 sequences. (Running on oeis4.)