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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 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.)