A188135 - OEIS

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

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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

Kelvin Voskuijl, Table of n, a(n) for n = 0..10000

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(2*n). (End)

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

MATHEMATICA