A061804 a(n) = 2*n*(2*n^2 + 1).

0, 6, 36, 114, 264, 510, 876, 1386, 2064, 2934, 4020, 5346, 6936, 8814, 11004, 13530, 16416, 19686, 23364, 27474, 32040, 37086, 42636, 48714, 55344, 62550, 70356, 78786, 87864, 97614, 108060, 119226, 131136, 143814, 157284, 171570, 186696, 202686, 219564

Offset: 0

Author

Amarnath Murthy, May 28 2001

Keywords

• nonn
• easy

Comments

Sum of n-th row of triangle of even numbers: (2, 4), (6, 8, 10, 12), (14, 16, 18, 20, 22, 24), (26, 28, 30, 32, 34, 36, 38, 40), ..., where n-th row contains 2n terms.

Also, integer values of n^3/2 + n. - Arkadiusz Wesolowski, Jul 20 2012

Examples

			a(3) = 114 = 14 + 16 + 18 + 20 + 22 + 24.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A002061, A005900.

Programs

Maple

A061804:=n->2*n*(2*n^2 + 1); seq(A061804(n), n=0..50); # Wesley Ivan Hurt, Mar 20 2014

Mathematica

Table[2*n*(2*n^2 + 1),{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Dec 04 2010 *)
LinearRecurrence[{4,-6,4,-1},{0,6,36,114},40] (* Harvey P. Dale, Feb 04 2023 *)

PARI

a(n) = { 2*n*(2*n^2 + 1) } \\ Harry J. Smith, Jul 28 2009

Python

def A061804(n): return n*((n**2<<2) + 2) # Chai Wah Wu, Aug 29 2022

Formula

a(n) = 6*A005900(n).

G.f.: 6*x*(1 + x)^2/(1 - x)^4. - Colin Barker, Apr 20 2012

a(n) = A002061(A002061(n+1)) - A002061(A002061(n)). - Daniel Poveda Parrilla, Jun 10 2017

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Alford Arnold, May 29 2001

Better description from Dean Hickerson, Jun 05 2001