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

0,2

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

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).

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

Example

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

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 *)

Prog

(PARI) { for (n=0, 1000, write("b061804.txt", 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

Crossrefs

Cf. A002061, A005900.

Sequence in context: A207437 A199243 A172137 * A207421 A207427 A207712

Adjacent sequences: A061801 A061802 A061803 * A061805 A061806 A061807

Keyword

nonn,easy

Author

Amarnath Murthy, May 28 2001

Extensions

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

Better description from Dean Hickerson, Jun 05 2001

Status

approved