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

1,3

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A198988 A098367 A141228 * A258718 A378353 A019864

Adjacent sequences: A133817 A133818 A133819 * A133821 A133822 A133823

Keyword

easy,nonn,tabl

Author

Peter Bala, Sep 25 2007

Extensions

Offset changed by Reinhard Zumkeller, Nov 11 2012

Status

approved