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A061804
a(n) = 2*n*(2*n^2 + 1).
5
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
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
Sequence in context: A207437 A199243 A172137 * A207421 A207427 A207712
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