A249356 8*A200975(n)-7 where A200975 are the numbers on the diagonals in Ulam's spiral.

1, 17, 33, 49, 65, 97, 129, 161, 193, 241, 289, 337, 385, 449, 513, 577, 641, 721, 801, 881, 961, 1057, 1153, 1249, 1345, 1457, 1569, 1681, 1793, 1921, 2049, 2177, 2305, 2449, 2593, 2737, 2881, 3041, 3201, 3361, 3521, 3697, 3873, 4049, 4225, 4417, 4609, 4801

Offset

1,2

Comments

All elements are odd.

The pair (a(n), a(n+1)) is separated by A002265(n-1) elements in A158057.

Links

Todd Silvestri, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Formula

a(n) = 2*n*(n+2)+(-1)^n-4*sin((Pi*n)/2).

G.f.: - x*(x^5-x^4+15*x+1)/((x-1)^3*(x^3+x^2+x+1)).

a(n) = 2*a(n-1) - a(n-2) + 16 if n == 2 mod 4, a(n) = 2*a(n-1) - a(n-2) otherwise. - Robert Israel, Nov 04 2014

a(n) = 2*n*(n+2) - (1-(-1)^n)*(1-2*i^(n+1)) + 1, where i=sqrt(-1). - Bruno Berselli, Nov 18 2014

Maple

seq(2*n*(n+2)+(-1)^n-4*sin((Pi*n)/2), n=1..100); # Robert Israel, Nov 04 2014

Mathematica

a[n_Integer/; n>0]:=2 n (n+2)+(-1)^n-4 Mod[n^2 (3 n+2), 4, -1]
CoefficientList[Series[-(x^5 - x^4 + 15 x + 1) / ((x - 1)^3 (x^3 + x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 16 2014 *)
Table[2 n (n + 2) - (1 - (-1)^n) (1 - 2 I^(n + 1)) + 1, {n, 1, 50}] (* Bruno Berselli, Nov 18 2014 *)
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 17, 33, 49, 65, 97}, 50] (* Harvey P. Dale, Sep 29 2019 *)

Prog

(PARI) a(n) = 2*n*(n+2)+(-1)^n-4*round(sin((Pi*n)/2)) \\ Charles R Greathouse IV, Nov 17 2014

Crossrefs

Sequence in context: A044062 A044443 A158057 * A329919 A346528 A286679

Adjacent sequences: A249353 A249354 A249355 * A249357 A249358 A249359

Keyword

nonn,easy

Author

Todd Silvestri, Oct 27 2014

Status

approved