A081346 First column in maze arrangement of natural numbers A081344.

1, 2, 9, 10, 25, 26, 49, 50, 81, 82, 121, 122, 169, 170, 225, 226, 289, 290, 361, 362, 441, 442, 529, 530, 625, 626, 729, 730, 841, 842, 961, 962, 1089, 1090, 1225, 1226, 1369, 1370, 1521, 1522, 1681, 1682, 1849, 1850, 2025, 2026, 2209, 2210, 2401, 2402, 2601

Offset

0,2

Comments

Interleaves odd squares A016754 with central polygonal numbers A001844.

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(n) = n^2 + n + 1 + n*(-1)^n.

a(2*n) = A016754(n), a(2*n+1) = 2*A001844(n).

G.f.: (1 + x + 5*x^2 - x^3 + 2*x^4)/((1-x)^3*(1+x)^2). - Colin Barker, Sep 03 2012

From Amiram Eldar, Feb 03 2026: (Start)

Sum_{n>=0} 1/a(n) = Pi^2/8 + tanh(Pi/2)*Pi/4.

Sum_{n>=0} (-1)^n/a(n) = Pi^2/8 - tanh(Pi/2)*Pi/4. (End)

Mathematica

a[n_] := n^2 + n + 1 + n*(-1)^n; Array[a, 51, 0] (* Amiram Eldar, Feb 03 2026 *)

Prog

(Magma) [n^2+n+1+n*(-1)^n: n in [0..50]]; // Vincenzo Librandi, Sep 05 2011

Crossrefs

Cf. A001844, A016754, A081345.

Sequence in context: A005695 A079747 A191576 * A301872 A290592 A058551

Adjacent sequences: A081343 A081344 A081345 * A081347 A081348 A081349

Keyword

easy,nonn

Author

Paul Barry, Mar 19 2003

Status

approved