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A033505 Expansion of 1/(1 - 3*x - x^2 + x^3). 8
1, 3, 10, 32, 103, 331, 1064, 3420, 10993, 35335, 113578, 365076, 1173471, 3771911, 12124128, 38970824, 125264689, 402640763, 1294216154, 4160024536, 13371648999, 42980755379, 138153890600, 444070778180, 1427385469761, 4588073296863, 14747534582170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

N. J. A. Sloane Notes on A030186 and A033505

Richard M. Low and Ardak Kapbasov, Non-Attacking Bishop and King Positions on Regular and Cylindrical Chessboards, Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.1, Table 4.

Index entries for linear recurrences with constant coefficients, signature (3,1,-1).

FORMULA

a(n) = 3*a(n-1) + a(n-2) - a(n-3). - Greg Dresden, Aug 16 2018

MATHEMATICA

CoefficientList[Series[1/(1 - 3 x - x^2 + x^3), {x, 0, 33}], x] (* or *) LinearRecurrence[{3, 1, -1}, {1, 3, 10}, 30] (* Vincenzo Librandi, Aug 17 2018 *)

PROG

(MAGMA) I:=[1, 3, 10]; [n le 3 select I[n] else 3*Self(n-1)+Self(n-2)-Self(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 17 2018

CROSSREFS

Partial sums of A030186.

Sequence in context: A077826 A292398 A273351 * A297067 A063782 A071718

Adjacent sequences:  A033502 A033503 A033504 * A033506 A033507 A033508

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 13 2002

STATUS

approved

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Last modified March 22 12:46 EDT 2019. Contains 321421 sequences. (Running on oeis4.)