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

0,1

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) + 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

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