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 A179436 a(n) = (3*n+7)*(3*n+2)/2. 2
 7, 25, 52, 88, 133, 187, 250, 322, 403, 493, 592, 700, 817, 943, 1078, 1222, 1375, 1537, 1708, 1888, 2077, 2275, 2482, 2698, 2923, 3157, 3400, 3652, 3913, 4183, 4462, 4750, 5047, 5353, 5668, 5992, 6325, 6667, 7018, 7378, 7747, 8125, 8512, 8908, 9313, 9727, 10150 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Trisection of A055998. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Leo Tavares, Illustration: Triangulated Triangles. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (-7-4*x+2*x^2)/(x-1)^3. a(n) = a(n-1)+9*(n+1) = (14+27*n+9*n^2)/2. a(n) = 2*a(n-1)-a(n-2) +9. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). a(n) mod 9 = A153466(n) mod 9 = 7. Sum_{n>=0} 1/a(n) = 1/2-2*Pi*sqrt(3)/45 = 0.2581600... - R. J. Mathar, Apr 07 2011 a(n) = A133694(n+1) + 6*A000217(n+1). - Leo Tavares, Mar 24 2022 Sum_{n>=0} (-1)^n/a(n) = 3/10 - 4*log(2)/15. - Amiram Eldar, Mar 27 2022 MAPLE A179436:=n->(3*n+7)*(3*n+2)/2: seq(A179436(n), n=0..100); # Wesley Ivan Hurt, Apr 24 2017 MATHEMATICA a[n_] := (3*n + 7)*(3*n + 2)/2; Array[a, 50, 0] (* Amiram Eldar, Mar 27 2022 *) PROG (Magma) [(3*n+7)*(3*n+2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 04 2011 (PARI) a(n)=(3*n+7)*(3*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A055998, A153466. Cf. A133694, A000217. Sequence in context: A137380 A309901 A094672 * A254963 A304075 A357196 Adjacent sequences: A179433 A179434 A179435 * A179437 A179438 A179439 KEYWORD nonn,easy AUTHOR Paul Curtz, Jan 12 2011 STATUS approved

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Last modified September 21 06:04 EDT 2023. Contains 365486 sequences. (Running on oeis4.)