A132127 a(n) = (n^3 + 3*n - 2)/2.

1, 6, 17, 37, 69, 116, 181, 267, 377, 514, 681, 881, 1117, 1392, 1709, 2071, 2481, 2942, 3457, 4029, 4661, 5356, 6117, 6947, 7849, 8826, 9881, 11017, 12237, 13544, 14941, 16431, 18017, 19702, 21489, 23381, 25381, 27492, 29717, 32059, 34521, 37106, 39817, 42657, 45629

Offset

1,2

Comments

Binomial transform of [1, 5, 6, 3, 0, 0, 0, ...].

Sum of the numbers in the top row and 1st column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows (see example). - Wesley Ivan Hurt, May 18 2021

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(n) = n*(n^2 + 3)/2 - 1.

Example

From Wesley Ivan Hurt, May 18 2021: (Start)
Sum of the numbers in the top row and 1st column.
                                                      [1   2  3  4  5]
                                      [1   2  3  4]   [6   7  8  9 10]
                            [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
                   [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
           [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
------------------------------------------------------------------------
  n         1        2         3            4                 5
------------------------------------------------------------------------
  a(n)      1        6        17           37                69
------------------------------------------------------------------------
(End)

Mathematica

Table[n*(n^2 + 3)/2 - 1, {n, 80}] (* Wesley Ivan Hurt, May 18 2021 *)

Prog

(PARI) a(n) = (n^3 + 3*n - 2)/2; \\ Andrew Howroyd, Apr 17 2021

Crossrefs

Row sums of triangle A132119 and A132128.

Sequence in context: A023663 A048208 A212980 * A023621 A000385 A192756

Adjacent sequences: A132124 A132125 A132126 * A132128 A132129 A132130

Keyword

nonn,easy

Author

Gary W. Adamson, Aug 10 2007

Extensions

Edited and terms a(13) and beyond from Andrew Howroyd, Apr 17 2021

Status

approved