A274602 Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.

0, 1, 1, 2, 5, 2, 3, 11, 9, 3, 4, 19, 20, 13, 4, 5, 29, 35, 29, 17, 5, 6, 41, 54, 51, 38, 21, 6, 7, 55, 77, 79, 67, 47, 25, 7, 8, 71, 104, 113, 104, 83, 56, 29, 8, 9, 89, 135, 153, 149, 129, 99, 65, 33, 9, 10, 109, 170, 199, 202, 185, 154, 115, 74, 37, 10

Offset

1,4

Comments

Mirrored version of a(n) is T(n,k) = (n-k)*(k+1)^2+k, 0 <= k <= n, read by rows:

0

1 1

2 5 2

3 9 11 3

4 13 20 19 4

5 17 29 35 29 5

As an infinite square array (matrix) with comments:

0 1 2 3 4 5 A001477

1 5 11 19 29 41 A028387

2 9 20 35 54 77 A014107

3 13 29 51 79 113 A144391

4 17 38 67 104 149 A182868

5 21 47 83 129 185

Links

Table of n, a(n) for n=1..66.

Example

0; 1,1; 2,5,2; 3,11,9,3; 4,19,20,13,4; 5,29,35,29,17,5; ...
As an infinite triangular array:
0
1   1
2   5   2
3  11   9    3
4  19  20   13    4
5  29  35   29   17    5
As an infinite square array (matrix) with comments:
0   1   2    3    4    5                   A001477
1   5   9   13   17   21                   A016813
2  11  20   29   38   47                   A017185
3  19  35   51   67   83
4  29  54   79  104  129
5  41  77  113  149  185

Mathematica

Table[k (n - k + 1)^(k + #) + n - k &[2 - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Dec 02 2016 *)

Prog

(Magma) /* As triangle */ [[k*(n-k+1)^2+n-k: k in [0..n]]: n in [0..10]];

Crossrefs

Cf. A002064, A001477, A016813, A017185, A062158 (central column). A028387, A014107, A144391, A182868.

Cf. Triangle read by rows: T(n,k) = k*(n-k+1)^m+n-k, 0 <= k <= n: A003056 (m = 0), A059036 (m = 1), A278910 (m = k).

Sequence in context: A083381 A197180 A129396 * A153289 A161643 A196982

Adjacent sequences: A274599 A274600 A274601 * A274603 A274604 A274605

Keyword

nonn,tabl

Author

Juri-Stepan Gerasimov, Dec 01 2016

Status

approved