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 A069497 Triangular numbers of the form 6k. 3
 0, 6, 36, 66, 78, 120, 210, 276, 300, 378, 528, 630, 666, 780, 990, 1128, 1176, 1326, 1596, 1770, 1830, 2016, 2346, 2556, 2628, 2850, 3240, 3486, 3570, 3828, 4278, 4560, 4656, 4950, 5460, 5778, 5886, 6216, 6786, 7140, 7260, 7626, 8256, 8646, 8778, 9180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = A000217(A112652(n+1)-1). - R. J. Mathar, Aug 21 2007 From R. J. Mathar, Nov 18 2009: (Start) a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 7*a(n-4) + 5*a(n-5) - 3*a(n-6) + a(n-7). G.f.: 6*x*(x^2-x+1)*(x^2+4*x+1)/((1+x^2)^2*(1-x)^3) (6*A154293). (End) MAPLE a[0] := 0:a[1] := 3:a[2] := 8:a[3] := 11:seq((12*(floor(i/4))+a[i mod 4])*(12*(floor(i/4))+a[i mod 4]+1)/2, i=1..100); MATHEMATICA CoefficientList[ Series[ 6x (x^2 -x +1) (x^2 +4x +1)/((x^2 +1)^2*(1 -x)^3), {x, 0, 45}], x] (* or *) LinearRecurrence[{3, -5, 7, -7, 5, -3, 1}, {0, 6, 36, 66, 78, 120, 210}, 46] (* Robert G. Wilson v, May 31 2017 *) Select[Accumulate[Range[0, 89]], Divisible[#, 6] &] (* Alonso del Arte, May 31 2017 *) CROSSREFS Sequence in context: A226119 A036148 A134639 * A139249 A070150 A161144 Adjacent sequences:  A069494 A069495 A069496 * A069498 A069499 A069500 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Mar 30 2002 EXTENSIONS More terms from Sascha Kurz, Apr 01 2002 More terms from R. J. Mathar, Aug 21 2007 STATUS approved

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Last modified June 19 09:43 EDT 2021. Contains 345126 sequences. (Running on oeis4.)