A127735 -id:A127735 - cp's OEIS frontend

A127736 a(n) = n(n^2 + 2n - 1)/2.

1, 7, 21, 46, 85, 141, 217, 316, 441, 595, 781, 1002, 1261, 1561, 1905, 2296, 2737, 3231, 3781, 4390, 5061, 5797, 6601, 7476, 8425, 9451, 10557, 11746, 13021, 14385, 15841, 17392, 19041, 20791, 22645, 24606, 26677, 28861, 31161, 33580, 36121, 38787, 41581

Offset: 1

Gary W. Adamson, Jan 26 2007

Row sums of A127735.
Row sums of A162610. - Reinhard Zumkeller, Jan 19 2013
For n  > 0, a(n) is the number of compositions of n+10 into n parts avoiding parts 2 and 3. - Milan Janjic, Jan 07 2016
Sum of the numbers in the top row and 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)
Add all the numbers in the top row and last 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        7        21           46                85
------------------------------------------------------------------------
(End)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A002260, A127701, A127735, A131416.

A127736:=n->n*(n^2+2*n-1)/2; seq(A127736(n), n=1..40); # Wesley Ivan Hurt, Mar 14 2014

Table[n*(n^2 + 2*n - 1)/2, {n, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)
CoefficientList[Series[-(x^2 - 3 x - 1)/(x - 1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 14 2014 *)
LinearRecurrence[{4,-6,4,-1},{1,7,21,46},60] (* Harvey P. Dale, Apr 22 2014 *)

Vec(-x*(x^2-3*x-1)/(x-1)^4 + O(x^100)) \\ Colin Barker, Mar 12 2014

a(n) = n*(n^2+2*n-1)/2; \\ Altug Alkan, Jan 07 2016

Row sums of triangle A131416. 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. (End)
a(n) = A057145(n+5,n). - R. J. Mathar, Jul 28 2016

More terms and new name from R. J. Mathar, Jul 21 2009

A131416 (A000012 * A002260) + (A002260 * A000012) - A000012.

Original entry on oeis.org

1, 4, 3, 8, 8, 5, 13, 14, 12, 7, 19, 21, 20, 16, 9, 26, 29, 29, 26, 20, 11, 34, 38, 39, 37, 32, 24, 13, 43, 48, 50, 49, 45, 38, 28, 15, 53, 59, 62, 62, 59, 53, 44, 32, 17, 64, 71, 75, 76, 74, 69, 61, 50, 36, 19

Offset: 1

Gary W. Adamson, Jul 08 2007

Left column = A034856: (1, 4, 8, 13, 19, 26, 34,...). Row sums = A127735: (1, 7, 21, 46, 85...).

			First few rows of the triangle are:
1;
4, 3;
8, 8, 5;
13, 14, 12, 7;
19, 21, 20, 16, 9;
26, 29, 29, 26, 20, 11;
...

Cf. A002260, A034856, A127735, A000012.

(A000012 * A002260) + (A002260 * A000012) - A000012; as infinite lower triangular matrices.

cp's OEIS Frontend

A127736 a(n) = n(n^2 + 2n - 1)/2.

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A131416 (A000012 * A002260) + (A002260 * A000012) - A000012.

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cp's OEIS Frontend

A127736 a(n) = n*(n^2 + 2*n - 1)/2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI

Formula

Extensions

A131416 (A000012 * A002260) + (A002260 * A000012) - A000012.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A127736 a(n) = n(n^2 + 2n - 1)/2.