A188135 a(n) = 8*n^2 + 2*n + 1.

1, 11, 37, 79, 137, 211, 301, 407, 529, 667, 821, 991, 1177, 1379, 1597, 1831, 2081, 2347, 2629, 2927, 3241, 3571, 3917, 4279, 4657, 5051, 5461, 5887, 6329, 6787, 7261, 7751, 8257, 8779, 9317, 9871, 10441, 11027, 11629, 12247, 12881

Offset

0,2

Comments

Bisection of A193867. - Omar E. Pol, Aug 16 2011

Sequence found by reading the line from 1, in the direction 1, 11, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011

Links

Table of n, a(n) for n=0..40.

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

Formula

First differences: a(n) - a(n-1) = 16*n - 6 = A113770(n) = 2*A004770(n).

Second differences: a(n) - 2*a(n-1) + a(n-2) = 16.

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

From R. J. Mathar, Apr 06 2011: (Start)

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

a(n) = A084849(2n). (End)

Prog

(Magma) [1 + 2*n + 8*n^2: n in [0..50]]; // Vincenzo Librandi, Mar 30 2011
(PARI) a(n)=8*n^2+2*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A185438.

Sequence in context: A160023 A263201 A337832 * A188382 A090950 A217947

Adjacent sequences: A188132 A188133 A188134 * A188136 A188137 A188138

Keyword

nonn,easy

Author

Paul Curtz, Mar 30 2011

Status

approved