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A081347 First column in maze arrangement of natural numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A074347 A102034 A102150

Adjacent sequences:  A081344 A081345 A081346 * A081348 A081349 A081350

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 19 2003

STATUS

approved

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Last modified February 20 16:25 EST 2018. Contains 299380 sequences. (Running on oeis4.)