A081347 First column in maze arrangement of natural numbers.

1, 2, 3, 12, 13, 30, 31, 56, 57, 90, 91, 132, 133, 182, 183, 240, 241, 306, 307, 380, 381, 462, 463, 552, 553, 650, 651, 756, 757, 870, 871, 992, 993, 1122, 1123, 1260, 1261, 1406, 1407, 1560, 1561, 1722, 1723, 1892, 1893, 2070, 2071, 2256, 2257, 2450, 2451

Offset: 0

Author

Paul Barry, Mar 19 2003

Keywords

• easy
• nonn

Comments

Interleaves two times the hexagonal numbers A000384 with A054554.

Examples

			Starting with 1,2,3, turn (LL) and then repeat (RRR)(LLL) to get
1 6 7 20
2 5 8 19
3 4 9 18
12 11 10 17
		

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. A081348, A080335.

Programs

Magma

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

Mathematica

CoefficientList[Series[(1 + x - x^2 + 7 x^3) / ((1 - x)^3 (1 + x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)
LinearRecurrence[{1,2,-2,-1,1},{1,2,3,12,13},60] (* Harvey P. Dale, Aug 13 2025 *)

Formula

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

a(2n) = A054554(n).

a(2n+1) = 2*A000384(n).

G.f.: (1+x-x^2+7*x^3)/((1-x)^3*(1+x)^2). [Colin Barker, Apr 17 2012]