A144670 -id:A144670 - cp's OEIS frontend

A162262 a(n) = (2n^3 + 5n^2 - 13*n)/2.

-3, 5, 30, 78, 155, 267, 420, 620, 873, 1185, 1562, 2010, 2535, 3143, 3840, 4632, 5525, 6525, 7638, 8870, 10227, 11715, 13340, 15108, 17025, 19097, 21330, 23730, 26303, 29055, 31992, 35120, 38445, 41973, 45710, 49662, 53835, 58235, 62868, 67740

Offset: 1

Vincenzo Librandi, Jun 29 2009

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

Cf. A144670.

LinearRecurrence[{4, -6, 4, -1}, {-3, 5, 30, 78}, 50] (* or *) CoefficientList[Series[(-3+17*x-8*x^2)/(1-x)^4,{x,0,50}],x] (* Vincenzo Librandi, Mar 04 2012 *)
Table[(2n^3+5n^2-13n)/2,{n,60}] (* Harvey P. Dale, Jul 03 2023 *)

Row sums from A144670: a(n) = Sum_{m=1..n} (2*m*n + m + n - 7).
From Vincenzo Librandi, Mar 05 2012: (Start)
G.f.: x*(-3 + 17*x - 8*x^2)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

New name from Vincenzo Librandi, Mar 05 2012

A324937 Triangle read by rows: T(n, k) = 2nk + n + k - 8.

Original entry on oeis.org

-4, -1, 4, 2, 9, 16, 5, 14, 23, 32, 8, 19, 30, 41, 52, 11, 24, 37, 50, 63, 76, 14, 29, 44, 59, 74, 89, 104, 17, 34, 51, 68, 85, 102, 119, 136, 20, 39, 58, 77, 96, 115, 134, 153, 172, 23, 44, 65, 86, 107, 128, 149, 170, 191, 212, 26, 49, 72, 95, 118, 141, 164, 187, 210, 233, 256

Offset: 1

Vincenzo Librandi, Mar 25 2019

			Triangle begins:
  -4;
  -1, 4;
   2, 9,  16;
   5, 14, 23, 32;
   8, 19, 30, 41, 52;
  11, 24, 37, 50, 63, 76;
  14, 29, 44, 59, 74, 89,  104;
  17, 34, 51, 68, 85, 102, 119, 136;
  20, 39, 58, 77, 96, 115, 134, 153, 172;  etc.

Similar sequence T(n,k) = 2*n*k+n+k-h: A144562 (h=1); A154680 (h=2); A154684 (h=3); A155724 (h=4); A155546 (h=5); A155550 (h=6); A144670 (h=7); this sequence (h=8); A155551 (h=9).

[2*n*k+n+k-8: k in [1..n], n in [1..11]]; /* As triangle */ [[2*n*k+n+k-8: k in [1..n]]: n in [1.. 15]];

t[n_, k_]:=2 n k + n + k - 8; Table[t[n, k], {n, 11}, {k, n}]//Flatten

G.f.: x*y*(9*x^3*y^2 - 4*x^2*y*(5 + 2*y) + x*(7 + 16*y) - 4)/((1 - x)^2*(1 - x*y)^3). - Stefano Spezia, Jul 29 2025

cp's OEIS Frontend

A162262 a(n) = (2n^3 + 5n^2 - 13*n)/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A324937 Triangle read by rows: T(n, k) = 2nk + n + k - 8.

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Mathematica

Formula

cp's OEIS Frontend

A162262 a(n) = (2*n^3 + 5*n^2 - 13*n)/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A324937 Triangle read by rows: T(n, k) = 2*n*k + n + k - 8.

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Mathematica

Formula

A162262 a(n) = (2n^3 + 5n^2 - 13*n)/2.

A324937 Triangle read by rows: T(n, k) = 2nk + n + k - 8.