A069011 Triangle with T(n,k) = n^2 + k^2.

0, 1, 2, 4, 5, 8, 9, 10, 13, 18, 16, 17, 20, 25, 32, 25, 26, 29, 34, 41, 50, 36, 37, 40, 45, 52, 61, 72, 49, 50, 53, 58, 65, 74, 85, 98, 64, 65, 68, 73, 80, 89, 100, 113, 128, 81, 82, 85, 90, 97, 106, 117, 130, 145, 162, 100, 101, 104, 109, 116, 125, 136, 149, 164, 181

Offset

0,3

Comments

For any i,j >=0 a(i)*a(j) is a member of this sequence, since (a^2 + b^2)*(c^2 + d^2) = (a*c + b*d)^2 + (a*d - b*c)^2. - Boris Putievskiy, May 05 2013

A227481(n) = number of squares in row n. - Reinhard Zumkeller, Oct 11 2013

Links

Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

Formula

T(n+1,k+1) = T(n,k) + 2*(n+k+1), k=0..n; T(n+1,0) = T(n,0) + 2*n + 1. - Reinhard Zumkeller, Oct 11 2013

Example

Rows start 0; 1,2; 4,5,8; 9,10,13,18; 16,17,20,25,32; etc.

Prog

(Haskell)
a069011 n k = a069011_tabl !! n !! k
a069011_row n = a069011_tabl !! n
a069011_tabl = map snd $ iterate f (1, [0]) where
   f (i, xs@(x:_)) = (i + 2, (x + i) : zipWith (+) xs [i + 1, i + 3 ..])
-- Reinhard Zumkeller, Oct 11 2013

Crossrefs

Cf. A001481 for terms in this sequence, A000161 for number of times each term appears, A048147 for square array.

Sequence in context: A034026 A125022 A362295 * A353386 A101185 A045702

Adjacent sequences: A069008 A069009 A069010 * A069012 A069013 A069014

Keyword

easy,nonn,tabl

Author

Henry Bottomley, Apr 02 2002

Status

approved