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A081270 Diagonal of triangular spiral in A051682. 2
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 January 29 01:35 EST 2020. Contains 331328 sequences. (Running on oeis4.)