A081348 First row in maze arrangement of natural numbers.

1, 6, 7, 20, 21, 42, 43, 72, 73, 110, 111, 156, 157, 210, 211, 272, 273, 342, 343, 420, 421, 506, 507, 600, 601, 702, 703, 812, 813, 930, 931, 1056, 1057, 1190, 1191, 1332, 1333, 1482, 1483, 1640, 1641, 1806, 1807, 1980, 1981, 2162, 2163, 2352, 2353, 2550

Offset

0,2

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) = (2*n^2+4*n+3-(2*n+1)(-1)^n)/2.

a(2*n) = A054569(n).

a(2*n+1) = 2*A014105(n+1).

G.f.: (1+5*x-x^2+3*x^3)/((1-x)^3*(1+x)^2). - Colin Barker, Apr 17 2012

Mathematica

CoefficientList[Series[(1 + 5 x - x^2 + 3 x^3) / ((1 - x)^3 (1 + x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Aug 08 2013 *)

Prog

(Magma) [(2*n^2+4*n+3-(2*n+1)*(-1)^n)/2: n in [0..50]]; // Vincenzo Librandi, Aug 08 2013

Crossrefs

Cf. A081347, A080335.

Sequence in context: A210605 A175262 A345911 * A002361 A041185 A042389

Adjacent sequences: A081345 A081346 A081347 * A081349 A081350 A081351

Keyword

easy,nonn

Author

Paul Barry, Mar 19 2003

Status

approved