A136392 a(n) = 6*n^2 - 10*n + 5.

1, 9, 29, 61, 105, 161, 229, 309, 401, 505, 621, 749, 889, 1041, 1205, 1381, 1569, 1769, 1981, 2205, 2441, 2689, 2949, 3221, 3505, 3801, 4109, 4429, 4761, 5105, 5461, 5829, 6209, 6601, 7005, 7421, 7849, 8289, 8741, 9205, 9681, 10169

Offset

1,2

Comments

Binomial transform of [1, 8, 12, 0, 0, 0, ...].

Numbers k such that 6*k - 5 is the square of a number of the form 6*k - 5, contained in A199859. - Eleonora Echeverri-Toro, Nov 29 2011

Central terms of the triangle A033292. - Reinhard Zumkeller, Feb 06 2012

Sequence found by reading the line from 1, in the direction 1, 9, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Jul 18 2012

Links

Table of n, a(n) for n=1..42.

John Elias, Illustration: Centered nesting cube frames.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = n*(3*n - 2) + (n-1)*(3*n - 5), n > 1.

a(n) = n*A016777(n-1) + (n-1)*A016777(n-2).

a(n) = a(n-1) + 12*n - 16 (with a(1)=1). - Vincenzo Librandi, Nov 24 2010

G.f.: x*(1+x)*(1+5*x)/(1-x)^3. - Colin Barker, Jan 09 2012

a(n) = 1 + A033580(n-1). - Omar E. Pol, Jul 18 2012

a(n) = A059722(n) - A059722(n-1). - J. M. Bergot, Nov 02 2012

a(n) = A000567(n-1) + A000567(n). - Charlie Marion, May 29 2024

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(2*x*(3*x - 2) + 5) - 5.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

Mathematica

Table[6n^2-10n+5, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 9, 29}, 50] (* Harvey P. Dale, Mar 05 2023 *)

Prog

(PARI) a(n)=6*n^2-10*n+5 \\ Charles R Greathouse IV, Nov 29 2011
(Haskell)
a136392 n = 2 * n * (3*n - 5) + 5 -- Reinhard Zumkeller, Feb 06 2012

Crossrefs

Cf. A000567, A001318, A016777, A033292, A033580, A059722, A199859, A201279, A204675.

Sequence in context: A031296 A146869 A129397 * A272732 A272740 A162263

Adjacent sequences: A136389 A136390 A136391 * A136393 A136394 A136395

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 28 2007

Status

approved