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

Author

Gary W. Adamson, Dec 28 2007

Keywords

• nonn
• easy

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

• John Elias, Illustration: Centered nesting cube frames.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

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

Programs

Haskell

a136392 n = 2 * n * (3*n - 5) + 5 -- Reinhard Zumkeller, Feb 06 2012

Mathematica

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

PARI

a(n)=6*n^2-10*n+5 \\ Charles R Greathouse IV, Nov 29 2011

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)