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 A133823 Triangle whose rows are sequences of increasing and decreasing cubes:1; 1,8,1; 1,8,27,8,1; ... . 4
 1, 1, 8, 1, 1, 8, 27, 8, 1, 1, 8, 27, 64, 27, 8, 1, 1, 8, 27, 64, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 343, 216, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 343, 512, 343, 216, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 343, 512, 729 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Reading the triangle by rows produces the sequence 1,1,8,1,1,8,27,8,1,..., analogous to A004737. T(n,k) = min(n,k)^3. The order of the list T(n,k) is by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1). - Boris Putievskiy, Jan 13 2013 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..9999 Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO] FORMULA O.g.f.: (1+qx)(1+4qx+q^2x^2)/((1-x)(1-qx)^3(1-q^2x)) = 1 + x(1 + 8q + q^2) + x^2(1 + 8q + 27q^2 + 8q^3 + q^4) + ... . From Boris Putievskiy, Jan 13 2013: (Start) a(n) = (A004737(n))^3. a(n) = (floor(sqrt(n-1)) - |n- floor(sqrt(n-1))^2- floor(sqrt(n-1))-1| +1)^3. (End) EXAMPLE Triangle starts 1; 1, 8, 1; 1, 8, 27, 8, 1; 1, 8, 27, 64, 27, 8, 1; From Boris Putievskiy, Jan 13 2013: (Start) The start of the sequence as table: 1...1...1...1...1...1... 1...8...8...8...8...8... 1...8..27..27..27..27... 1...8..27..64..64..64... 1...8..27..64.125.125... 1...8..27..64.125.216... . . . The start of the sequence as triangle array read by rows: 1; 1,8,1; 1,8,27,8,1; 1,8,27,64,27,8,1; 1,8,27,64,125,64,27,8,1; 1,8,27,64,125,216,125,64,27,8,1; . . . Row number k contains 2*k-1 numbers 1,8,...,(k-1)^3,k^3,(k-1)^3,...,8,1. (End) MATHEMATICA Table[Join[Range[n]^3, Range[n-1, 1, -1]^3], {n, 10}]//Flatten (* Harvey P. Dale, May 29 2019 *) CROSSREFS Cf. A004737, A037270 (row sums), A133820, A124258, A133824, A003983. Sequence in context: A178163 A197110 A109571 * A168643 A173742 A146881 Adjacent sequences:  A133820 A133821 A133822 * A133824 A133825 A133826 KEYWORD easy,nonn,tabf AUTHOR Peter Bala, Sep 25 2007 STATUS approved

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)