editing

approved

Row sums of triangle A134390A131416. Also, binomial transform of [1, 6, 8, 3, 0, 0, 0, ...). - Gary W. Adamson, Oct 23 2007

Cf. A002260, A127701, A127735, A134390A131416.

approved

editing

proposed

approved

editing

proposed

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

Row sums of triangle A134390. Also, binomial transform of [1, 6, 8, 3, 0, 0, 0, ...). - Gary W. Adamson, Oct 23 2007

a(n) = (n+1)*A000217(n) - n = A006002(n) - n. - R. J. Mathar, Jul 21 2009

From Colin Barker, Mar 12 2014: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). G.f.: -x*(x^2-3*x-1) / (x-1)^4. - _Colin Barker_, Mar 12 2014

G.f.: -x*(x^2-3*x-1) / (x-1)^4. (End)

approved

editing

editing

approved

Add all the numbers in the top row and last column.

a(n) is the sum Sum of all the numbers going across in the top row and down the last 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

From Wesley Ivan Hurt, May 18 2021: (Start)

[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 7 21 46 85

------------------------------------------------------------------------

(End)

a(n) is the sum of all the numbers going across the top row and down the last column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 18 2021

approved

editing

proposed

approved