A081353 Diagonal of square maze arrangement of natural numbers A081349.

3, 5, 13, 19, 31, 41, 57, 71, 91, 109, 133, 155, 183, 209, 241, 271, 307, 341, 381, 419, 463, 505, 553, 599, 651, 701, 757, 811, 871, 929, 993, 1055, 1123, 1189, 1261, 1331, 1407, 1481, 1561, 1639, 1723, 1805, 1893, 1979, 2071, 2161, 2257, 2351, 2451, 2549

Offset: 0

Author

Paul Barry, Mar 19 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A081349, A081350, A081351, A081352.

Cf. A109613, A137932.

Bisections are in A054554, A125202.

Programs

Magma

[(n + 1)*(n + 2) + (-1)^n: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

Maple

A081353:=n->(n+1)*(n+2)+(-1)^n: seq(A081353(n), n=0..100); # Wesley Ivan Hurt, Aug 09 2015

Mathematica

Table[(n + 1) (n + 2) + (-1)^n, {n, 0, 70}] (* Wesley Ivan Hurt, Aug 09 2015 *)
LinearRecurrence[{2,0,-2,1},{3,5,13,19},50] (* Harvey P. Dale, Aug 02 2021 *)

Formula

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

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

From Wesley Ivan Hurt, Aug 09 2015: (Start)

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4), n>4.

a(n) = n^2+3n+3 if n is even, otherwise n^2+3n+1.

a(n) = A137932(n+3) - A109613(n+1). (End)