A133820 Triangle whose rows are sequences of increasing cubes: 1; 1,8; 1,8,27; ... .

1, 1, 8, 1, 8, 27, 1, 8, 27, 64, 1, 8, 27, 64, 125, 1, 8, 27, 64, 125, 216, 1, 8, 27, 64, 125, 216, 343, 1, 8, 27, 64, 125, 216, 343, 512, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Offset: 1

Author

Peter Bala, Sep 25 2007

Keywords

• easy
• nonn
• tabl

Comments

Reading the triangle by rows produces the sequence 1,1,8,1,8,27,1,8,27,64,..., analogous to A002260.

Examples

			Triangle starts
1;
1, 8;
1, 8, 27;
1, 8, 27, 64;
1, 8, 27, 64, 125;
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Crossrefs

Cf. A000537 (row sums), A002260, A019522, A133819, A133821, A133823.

Programs

Haskell

a133820 n k = a133820_tabl !! (n-1) !! (k-1)
a133820_row n = a133820_tabl !! (n-1)
a133820_tabl = map (`take` (tail a000578_list)) [1..]
-- Reinhard Zumkeller, Nov 11 2012

Mathematica

Module[{nn=10,c},c=Range[nn]^3;Flatten[Table[Take[c,n],{n,10}]]] (* Harvey P. Dale, Mar 05 2014 *)

Formula

O.g.f.: (1+4qx+q^2x^2)/((1-x)(1-qx)^4) = 1 + x(1 + 8q) + x^2(1 + 8q + 27q^2) + ... .

Extensions

Offset changed by Reinhard Zumkeller, Nov 11 2012