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A177787 Number of paths from (0,0) to (n+2,n) using only up and right steps and avoiding two or more consecutive moves up or three or more consecutive moves right. 4
2, 5, 10, 18, 30, 47, 70, 100, 138, 185, 242, 310, 390, 483, 590, 712, 850, 1005, 1178, 1370, 1582, 1815, 2070, 2348, 2650, 2977, 3330, 3710, 4118, 4555, 5022, 5520, 6050, 6613, 7210, 7842, 8510, 9215, 9958, 10740, 11562, 12425, 13330, 14278, 15270 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Strings of length 2n+2 over the alphabet {U, R} with n Rs and avoiding UU or RRR as substrings.

Also number of binary words with 3 1's and n 0's that do not contain the substring 101. a(2) = 5: 00111, 10011, 11001, 11100, 01110. - Alois P. Heinz, Jul 18 2013

Let (b(n)) be the p-INVERT of A010892 using p(S) = 1 - S^2; then b(n) = a(n+1) for n >= 0. See A292301. - Clark Kimberling, Sep 30 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). - R. J. Mathar, May 22 2010

FORMULA

a(n) = 1/6 * n (11 + n^2).

From R. J. Mathar, May 22 2010: (Start)

a(n) = A140226(n)/2.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: x*(2-3*x+2*x^2)/(x-1)^4. (End)

MAPLE

a:= n-> n/6*(11+n^2): seq(a(n), n=1..40);

MATHEMATICA

CoefficientList[Series[(2-3*x+2*x^2)/(x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)

PROG

(MAGMA) I:=[2, 5, 10, 18]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jul 04 2012

CROSSREFS

First differences of A227161. - Alois P. Heinz, Jul 18 2013

Sequence in context: A146010 A077631 A025223 * A104688 A117485 A084835

Adjacent sequences:  A177784 A177785 A177786 * A177788 A177789 A177790

KEYWORD

nonn,easy

AUTHOR

Shanzhen Gao, May 13 2010

EXTENSIONS

More terms from R. J. Mathar, May 22 2010

STATUS

approved

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)