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 A081270 Diagonal of triangular spiral in A051682. 3
 3, 16, 38, 69, 109, 158, 216, 283, 359, 444, 538, 641, 753, 874, 1004, 1143, 1291, 1448, 1614, 1789, 1973, 2166, 2368, 2579, 2799, 3028, 3266, 3513, 3769, 4034, 4308, 4591, 4883, 5184, 5494, 5813, 6141, 6478, 6824, 7179, 7543, 7916, 8298, 8689, 9089, 9498 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Hacène Belbachir, Toufik Djellal, Jean-Gabriel Luque, On the self-convolution of generalized Fibonacci numbers, arXiv:1703.00323 [math.CO], 2017. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = A064226(n) + 2n. a(n) = 3C(n, 0)+13C(n, 1)+9C(n, 2); binomial transform of (3, 13, 9, 0, 0, 0, ...). a(n) = (9n^2+17n+6)/2. G.f.: (3+7x-x^2)/(1-x)^3. a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 08 2012 MATHEMATICA CoefficientList[Series[(3+7x-x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *) PROG (Magma) [(9*n^2+17*n+6)/2: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012 (PARI) a(n)=(9*n^2+17*n+6)/2 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A064226, A081268. Sequence in context: A196573 A196804 A280093 * A271374 A147874 A092466 Adjacent sequences: A081267 A081268 A081269 * A081271 A081272 A081273 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 15 2003 STATUS approved

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Last modified February 3 18:43 EST 2023. Contains 360044 sequences. (Running on oeis4.)