A095166 Group the natural numbers >= 1 so that the n-th group contains n(n+1)/2 numbers and obtain the group sum.

1, 9, 45, 155, 420, 966, 1974, 3690, 6435, 10615, 16731, 25389, 37310, 53340, 74460, 101796, 136629, 180405, 234745, 301455, 382536, 480194, 596850, 735150, 897975, 1088451, 1309959, 1566145, 1860930, 2198520, 2583416, 3020424, 3514665

Offset

1,2

Comments

Each group can be formed into a triangle.

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = (2*(n-1)^5 + 15*(n-1)^4 + 44*(n-1)^3 + 69*(n-1)^2 + 62*(n-1) + 24)/24. [corrected by Georg Fischer, May 08 2021]

Example

(1), (2, 3, 4), (5, 6, 7, 8, 9, 10), (11, 12, 13, 14, 15, 16, 17, 18, 19, 20), ...

Maple

seq((2*(n-1)^5 + 15*(n-1)^4 + 44*(n-1)^3 + 69*(n-1)^2 + 62*(n-1) + 24)/24, n=1..33); # Georg Fischer, May 08 2021

Mathematica

tetr[n_] := Binomial[n + 3, 3]; tri[n_] := (n(n + 1)/2); Table[ tri[ tetr[n]] - tri[ tetr[n - 1]], {n, 0, 32}] (* Robert G. Wilson v, Jun 05 2004 *)

Crossrefs

Cf. A000217, A000292.

Sequence in context: A060008 A212089 A212142 * A357717 A341988 A341069

Adjacent sequences: A095163 A095164 A095165 * A095167 A095168 A095169

Keyword

nonn

Author

Amarnath Murthy, Jun 01 2004

Extensions

Edited and extended by Robert G. Wilson v, Jun 05 2004

Status

approved