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A014494 Even triangular numbers. 11
0, 6, 10, 28, 36, 66, 78, 120, 136, 190, 210, 276, 300, 378, 406, 496, 528, 630, 666, 780, 820, 946, 990, 1128, 1176, 1326, 1378, 1540, 1596, 1770, 1830, 2016, 2080, 2278, 2346, 2556, 2628, 2850, 2926, 3160, 3240, 3486, 3570, 3828, 3916, 4186, 4278, 4560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Even numbers of the form n*(n+1)/2.

Even generalized hexagonal numbers. - Omar E. Pol, Apr 24 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

a(n) = (2*n+1)*(2*n+1-(-1)^n)/2. - Ant King, Nov 18 2010

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). - Ant King, Nov 18 2010

G.f.:-2*x*(3*x^2+2*x+3)/((x+1)^2*(x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

a(n) = A000217(A014601(n)). - Reinhard Zumkeller, Oct 04 2004

a(n) = A014493(n+1)-(2n+1)*(-1)^n. - R. J. Mathar, Sep 15 2009

a(n) = A193867(n+1) - 1. - Omar E. Pol, Aug 17 2011

MATHEMATICA

Table[2Ceiling[n/2]*(2n + 1), {n, 0, 47}] (* Robert G. Wilson v, Nov 05 2004 *)

1/2 (2#+1)(2#+1-(-1)^#) &/@Range[0, 47] (* Ant King, Nov 18 2010 *)

Select[1/2 #(#+1) &/@Range[0, 95], EvenQ] (* Ant King, Nov 18 2010 *)

PROG

(MAGMA) [1/2*(2*n+1)*(2*n+1-(-1)^n): n in [0..50]]; // Vincenzo Librandi, Aug 18 2011

(PARI) a(n)=(2*n+1)*(2*n+1-(-1)^n)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000217, A014493, A056575, A074378.

Cf. similar sequences listed in A299645.

Sequence in context: A184387 A295185 A225845 * A318894 A129545 A097578

Adjacent sequences:  A014491 A014492 A014493 * A014495 A014496 A014497

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)