A081350 First column in maze array of natural numbers A081349.

1, 2, 3, 4, 15, 16, 35, 36, 63, 64, 99, 100, 143, 144, 195, 196, 255, 256, 323, 324, 399, 400, 483, 484, 575, 576, 675, 676, 783, 784, 899, 900, 1023, 1024, 1155, 1156, 1295, 1296, 1443, 1444, 1599, 1600, 1763, 1764, 1935, 1936, 2115, 2116, 2303, 2304, 2499

Offset

0,2

Comments

Interleaves A000466 with even squares A016742.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(0) = 1, a(1) = 2, a(n) = (n-1)*(n+(-1)^n), n > 1.

G.f.: -(2*x^6-10*x^4+x^3+x^2-x-1)/((1-x)^3*(1+x)^2). - Colin Barker, Sep 03 2012

From Amiram Eldar, Feb 16 2026: (Start)

Sum_{n>=0} 1/a(n) = Pi^2/24 + 2.

Sum_{n>=0} (-1)^n/a(n) = 1 - Pi^2/24. (End)

Mathematica

a[n_] := (n-1)*(n+(-1)^n); a[0] = 1; a[1] = 2; Array[a, 100, 0] (* Amiram Eldar, Feb 16 2026 *)

Crossrefs

Cf. A000466, A016742, A081349, A081351, A081352.

Sequence in context: A334619 A037323 A065812 * A173320 A135633 A269725

Adjacent sequences: A081347 A081348 A081349 * A081351 A081352 A081353

Keyword

nonn,easy

Author

Paul Barry, Mar 19 2003

Status

approved