A133821 Triangle whose rows are sequences of increasing fourth powers: 1; 1,16; 1,16,81; ... .

1, 1, 16, 1, 16, 81, 1, 16, 81, 256, 1, 16, 81, 256, 625, 1, 16, 81, 256, 625, 1296, 1, 16, 81, 256, 625, 1296, 2401, 1, 16, 81, 256, 625, 1296, 2401, 4096, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000

Offset: 1

Author

Peter Bala, Sep 25 2007

Keywords

• easy
• nonn
• tabl

Comments

Reading the triangle by rows produces the sequence 1,1,16,1,16,81,1,16,81,256,..., analogous to A002260.

Examples

			Triangle starts
1;
1, 16;
1, 16; 81;
1, 16, 81, 256;
1, 16, 81, 256, 625;
		

Links

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

Crossrefs

Cf. A000538 (row sums), A002260, A133819, A133820, A133824.

Programs

Haskell

a133821 n k = a133821_tabl !! (n-1) !! (k-1)
a133821_row n = a133821_tabl !! (n-1)
a133821_tabl = map (`take` (tail a000583_list)) [1..]
-- Reinhard Zumkeller, Nov 11 2012

Mathematica

Module[{nn=10,fp},fp=Range[(nn(nn+1))/2]^4;Table[TakeList[fp,{n}],{n,nn}]]//Flatten (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Mar 29 2020 *)

Formula

O.g.f.: (1+11qx+11q^2x^2+q^3x^3)/((1-x)(1-qx)^5) = 1 + x(1 + 16q) + x^2(1 + 16q + 81q^2) + ... . Cf. 4th row of A008292.

Extensions

Offset changed by Reinhard Zumkeller, Nov 11 2012