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A182868
a(n) = -1 + n + 4*n^2.
3
-1, 4, 17, 38, 67, 104, 149, 202, 263, 332, 409, 494, 587, 688, 797, 914, 1039, 1172, 1313, 1462, 1619, 1784, 1957, 2138, 2327, 2524, 2729, 2942, 3163, 3392, 3629, 3874, 4127, 4388, 4657, 4934, 5219, 5512, 5813, 6122, 6439, 6764, 7097, 7438, 7787, 8144, 8509, 8882, 9263, 9652
OFFSET
0,2
COMMENTS
First quadrisection of A176126(n). Take clockwise (square) spiral from A023443(n)=n-1: a(n) is on the negative x-axis. Fourth quadrisection (-1-n+4*n^2) is on the negative y-axis.
Conjecture: the 4 quadrisections of (the family) A064038, A160050, A176126, A178242 (see A181407) come from square spiral.
a(n) mod 9 has period 9: 8,4,8,2,4,5,5,4,2. a(n) mod 10 has period 10: 9,4,7,8,7,4,9,2,3,2. Each polynomial modulo some constant c has a period of length c (and perhaps shorter ones). - Paul Curtz and Bruno Berselli, Feb 05 2011
FORMULA
a(n) = A176126(4*n).
a(n) = 4*n^2 + n - 1.
a(n) = a(n-1) - 3 + 8*n.
a(n) = 2*a(n) - a(n-2) + 8.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: -(1 - 7*x - 2*x^2)/(1-x)^3. - Bruno Berselli, Feb 05 2011
MATHEMATICA
f[n_]:=-1+n+4*n^2; f[Range[0, 100]] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
PROG
(Magma) [-1+n+4*n^2: n in [0..700] ] // Vincenzo Librandi, Feb 01 2011
(PARI) a(n)=-1+n+4*n^2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A173511 A218925 A356347 * A178947 A041859 A022266
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Feb 01 2011
STATUS
approved