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

0,2

Comments

Interleaves two times the hexagonal numbers A000384 with A054554.

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) = ((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]

Example

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

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 *)

Prog

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

Crossrefs

Cf. A081348, A080335.

Sequence in context: A157900 A157902 A102660 * A309176 A074347 A102034

Adjacent sequences: A081344 A081345 A081346 * A081348 A081349 A081350

Keyword

easy,nonn

Author

Paul Barry, Mar 19 2003

Status

approved