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, 13531, 14197, 14879, 15577, 16291, 17021, 17767

Offset: 0

Author

Paul Curtz, Mar 30 2011

Keywords

• nonn
• easy
• changed

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

• Kelvin Voskuijl, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A004770, A084849, A113770, A185438, A193867.

Programs

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

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(2*n). (End)

E.g.f.: exp(x)*(1 + 10*x + 8*x^2). - Elmo R. Oliveira, Oct 19 2024

Extensions

a(41)-a(47) from Elmo R. Oliveira, Oct 19 2024