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A068912 Number of n step walks (each step +/-1 starting from 0) which are never more than 3 or less than -3. 6
1, 2, 4, 8, 14, 28, 48, 96, 164, 328, 560, 1120, 1912, 3824, 6528, 13056, 22288, 44576, 76096, 152192, 259808, 519616, 887040, 1774080, 3028544, 6057088, 10340096, 20680192, 35303296, 70606592, 120532992, 241065984, 411525376, 823050752, 1405035520, 2810071040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..35.

T. Mansour, A. O. Munagi, Alternating subsets modulo m, Rocky Mt. J. Math. 42, No. 4, 1313-1325 (2012), Table 1 q=(0,1,1,1)

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-2).

FORMULA

G.f.: (1+2*x)/(1-4*x^2+2*x^4).

a(n) = A068913(3, n).

a(n) = 4*a(n-2) - 2*a(n-4).

a(2n) = A007070(n) = 2*a(2n-1)-A060995(n); a(2n+1) = 2*a(2n).

MATHEMATICA

nn=33; CoefficientList[Series[s+a + b + c + d + e +f/.Solve[{s ==1 + x a + x b, a==x s + x c, b==x s +x d, c==x a +x e, d== x b + x f, e==x c, f==x d, z==x e + x f }, {s, a, b, c, d, e, f, z}], {x, 0, nn}], x] (* Geoffrey Critzer, Jan 13 2014 *)

CROSSREFS

Cf. A000007, A016116 (without initial term), A068911, A068913 for similar.

Sequence in context: A196721 A118034 A096590 * A164176 A325860 A217932

Adjacent sequences:  A068909 A068910 A068911 * A068913 A068914 A068915

KEYWORD

nonn,walk,easy

AUTHOR

Henry Bottomley, Mar 06 2002

STATUS

approved

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Last modified September 15 16:33 EDT 2019. Contains 327078 sequences. (Running on oeis4.)