A081345 First row in maze arrangement of natural numbers A081344.

1, 4, 5, 16, 17, 36, 37, 64, 65, 100, 101, 144, 145, 196, 197, 256, 257, 324, 325, 400, 401, 484, 485, 576, 577, 676, 677, 784, 785, 900, 901, 1024, 1025, 1156, 1157, 1296, 1297, 1444, 1445, 1600, 1601, 1764, 1765, 1936, 1937, 2116, 2117, 2304, 2305, 2500

Offset: 0

Author

Paul Barry, Mar 19 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A081346.

Programs

Magma

[n^2+n+1-n*(-1)^n: n in [0..50]]; // Vincenzo Librandi, Aug 08 2013

Mathematica

CoefficientList[Series[(5 x^3 - x^2 + 3 x + 1) / ((1 - x)^3 (1 + x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)

Formula

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

a(2*n) = A053755(n), a(2*n+1) = 4 * A004120(n).

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