A085473 a(n) = 6*n^2 + 3*n + 1.

1, 10, 31, 64, 109, 166, 235, 316, 409, 514, 631, 760, 901, 1054, 1219, 1396, 1585, 1786, 1999, 2224, 2461, 2710, 2971, 3244, 3529, 3826, 4135, 4456, 4789, 5134, 5491, 5860, 6241, 6634, 7039, 7456, 7885, 8326, 8779, 9244, 9721, 10210, 10711, 11224, 11749, 12286, 12835

Offset

0,2

Comments

T(n,3) of A085475.

Sequence found by reading the line from 1, in the direction 1, 10,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 09 2011

Sums of the triangular numbers from A000217(2*n-1) to A000217(2*n+1), with A000217(-1) = 0. - Bruno Berselli, Sep 04 2018

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1 + 7*x + 4*x^2)/(1 - x)^3.

a(n) = binomial(2*n+3,3) - binomial(2*n,3).

a(n) = 12*n + a(n-1) - 3 for n > 0, a(0)=1. - Vincenzo Librandi, Aug 08 2010

a(0)=1, a(1)=10, a(2)=31; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Nov 15 2011

E.g.f.: exp(x)*(1 + 9*x + 6*x^2). - Elmo R. Oliveira, Oct 18 2024

Mathematica

Table[3 n (2 n + 1) + 1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
Table[Binomial[2 n + 3, 3] - Binomial[2 n, 3], {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 10, 31}, 50] (* Harvey P. Dale, Nov 15 2011 *)

Prog

(PARI) x='x+O('x^50); Vec((1+7*x+4*x^2)/(1-x)^3) \\ G. C. Greubel, Jun 13 2017
(PARI) for(n=0, 25, print1(6*n^2 + 3*n + 1, ", ")) \\ G. C. Greubel, Jun 13 2017

Crossrefs

Cf. A000217, A001318, A016813, A085474, A085475.

Sequence in context: A100500 A209994 A211013 * A051943 A059306 A192023

Adjacent sequences: A085470 A085471 A085472 * A085474 A085475 A085476

Keyword

nonn,easy

Author

Paul Barry, Jul 01 2003

Status

approved