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

Author

Paul Barry, Mar 19 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A081345.

Programs

Magma

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

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]