A064226 a(n) = (9*n^2 + 13*n + 6)/2.

3, 14, 34, 63, 101, 148, 204, 269, 343, 426, 518, 619, 729, 848, 976, 1113, 1259, 1414, 1578, 1751, 1933, 2124, 2324, 2533, 2751, 2978, 3214, 3459, 3713, 3976, 4248, 4529, 4819, 5118, 5426, 5743, 6069, 6404, 6748, 7101, 7463, 7834, 8214, 8603, 9001, 9408, 9824

Offset

0,1

Comments

Diagonal of triangular spiral in A051682. - Paul Barry, Mar 15 2003

Ehrhart polynomial of open quadrilateral with vertices (0,2),(2,3),(3,1),(2,0). - Michael Somos, Jul 22 2006

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Milan Janjic, Two Enumerative Functions.

National Security Agency, Intrigued? (advertisement), Notices of the American Mathematical Society, Vol. 49 (2002), p. 216.

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

Formula

From Paul Barry, Mar 15 2003: (Start)

a(n) = 3*C(n,0) + 11*C(n,1) + 9*C(n,2); binomial transform of (3, 11, 9, 0, 0, 0, ...).

G.f.: (3 + 5*x + x^2)/(1-x)^3.

a(n) = A081268(n) + 2. (End)

A064225(n) = a(-1-n). - Michael Somos, Jul 22 2006

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Apr 16 2023

E.g.f.: (3 + 11*x + 9*x^2/2)*exp(x). - Elmo R. Oliveira, Oct 21 2024

Maple

A064226:=n-> (9*n^2 + 13*n + 6) / 2; seq(A064226(n), n=0..50); # Wesley Ivan Hurt, May 08 2014

Mathematica

Table[(9 n^2 + 13 n + 6)/2, {n, 0, 50}] (* Wesley Ivan Hurt, May 08 2014 *)
LinearRecurrence[{3, -3, 1}, {3, 14, 34}, 50] (* Vincenzo Librandi, Jul 19 2015 *)

Prog

(PARI) {a(n) = 3 + n * (9*n + 13) / 2}; /* Michael Somos, Jul 22 2006 */
(Magma) I:=[3, 14, 34]; [n le 3 select I[n] else 3*Self(n-1) - 3*Self(n-2) + Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 19 2015

Crossrefs

Cf. A051682, A064225, A081267, A081268, A235332.

Sequence in context: A155154 A081269 A140064 * A077288 A094627 A009394

Adjacent sequences: A064223 A064224 A064225 * A064227 A064228 A064229

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 22 2001

Status

approved