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, 2501

Offset

0,2

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).

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

From Amiram Eldar, Feb 03 2026: (Start)

Sum_{n>=0} 1/a(n) = 1/2 + coth(Pi/2)*Pi/4 + Pi^2/24.

Sum_{n>=0} (-1)^n/a(n) = 1/2 + coth(Pi/2)*Pi/4 - Pi^2/24. (End)

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 *)

Prog

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

Crossrefs

Cf. A004120, A053755, A081344, A081346.

Sequence in context: A382218 A175263 A000695 * A137527 A024854 A309759

Adjacent sequences: A081342 A081343 A081344 * A081346 A081347 A081348

Keyword

easy,nonn

Author

Paul Barry, Mar 19 2003

Status

approved