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

0,1

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A081349, A081350, A081351, A081352.

Cf. A109613, A137932.

Bisections are in A054554, A125202.

Sequence in context: A019420 A306930 A019358 * A238092 A024820 A360884

Adjacent sequences: A081350 A081351 A081352 * A081354 A081355 A081356

Keyword

nonn,easy

Author

Paul Barry, Mar 19 2003

Status

approved