A377809 k*(k+3)/2 appears k times.

2, 5, 5, 9, 9, 9, 14, 14, 14, 14, 20, 20, 20, 20, 20, 27, 27, 27, 27, 27, 27, 35, 35, 35, 35, 35, 35, 35, 44, 44, 44, 44, 44, 44, 44, 44, 54, 54, 54, 54, 54, 54, 54, 54, 54, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 90

Offset

1,1

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = A002024(n)*(A002024(n)+3)/2.

First difference of A119713.

T(n,k) = A000096(n) for 1 <= k <= n. - Alois P. Heinz, Nov 09 2024

G.f.: x*y*(2 - x*y)/((1 - x)*(1 - x*y)^3). - Stefano Spezia, Nov 09 2024

Example

As triangle:
   2;
   5,  5;
   9,  9,  9;
  14, 14, 14, 14;
  20, 20, 20, 20, 20;
  ...

Mathematica

s={}; Do[AppendTo[s, Table[k(k+3)/2, k]], {k, 12}]; Flatten[s] (* James C. McMahon, Nov 09 2024 *)

Prog

(Python)
from math import isqrt
def A377809(n): return (r:=(m:=isqrt(k:=n<<1))+(k>m*(m+1)))*(r+3)>>1

Crossrefs

Cf. A000096, A002024, A119713.

Sequence in context: A200242 A062553 A126357 * A070243 A367642 A050175

Adjacent sequences: A377806 A377807 A377808 * A377810 A377811 A377812

Keyword

nonn,easy,tabl

Author

Chai Wah Wu, Nov 08 2024

Status

approved