A081270 Diagonal of triangular spiral in A051682.
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, 9916
Offset: 0
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).
Programs
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Magma
[(9*n^2+17*n+6)/2: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012
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Mathematica
CoefficientList[Series[(3+7x-x^2)/(1-x)^3,{x,0,50}],x] (* Vincenzo Librandi, Jul 08 2012 *) -
PARI
a(n)=(9*n^2+17*n+6)/2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = A064226(n) + 2*n.
a(n) = 3*binomial(n,0) + 13*binomial(n,1) + 9*binomial(n,2); binomial transform of (3, 13, 9, 0, 0, 0, ...).
a(n) = (9*n^2 + 17*n + 6)/2.
G.f.: (3 + 7*x - x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jul 08 2012
E.g.f.: exp(x)*(6 + 26*x + 9*x^2)/2. - Elmo R. Oliveira, Nov 13 2024