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A181510 Number of permutations of the multiset {1,1,2,2,3,3,...,n+1,n+1} avoiding the permutation patterns {132, 231, 2134} 7
6, 18, 34, 54, 78, 106, 138, 174, 214, 258, 306, 358, 414, 474, 538, 606, 678, 754, 834, 918, 1006, 1098, 1194, 1294, 1398, 1506, 1618, 1734, 1854, 1978 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is also the surface ares of the n-th solid in the following recursive construction:

The first solid is a unit cube (hence a(1)=6).

To form the n-th solid from the (n-1)st solid, construct a row of 2n-1 cubes, then center the (n-1)st solid on top of this row. (For example, the second solid is a row of 3 unit cubes, with a single unit cube centered on top of the middle cube. This construction has surface area a(2)=18.)

The sequence provides all nonnegative integers m such that 2*m+13 is a square. - Bruno Berselli, Mar 01 2013

LINKS

Table of n, a(n) for n=1..30.

Lara K. Pudwell, Stacking Blocks and Counting Permutations, Mathematics Magazine 83 (2010), 297-302.

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

FORMULA

a(n) = 2n^2+6n-2.

From Bruno Berselli, Oct 29 2010: (Start)

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

a(n) -3*a(n-1) +3*a(n-2) -a(n-3) = 0 for n>3.

a(n) = 2*A014209(n) = 2*A082111(n-1)+4 = A051936(2n+2)+n+4. (End)

EXAMPLE

For n=1, the permutations of {1,1,2,2} avoiding the patterns {132, 231, 2134} are {1122, 1212, 1221, 2112, 2121, 2211}.

For n=2, the permutations of {1,1,2,2,3,3} avoiding the patterns {132, 231, 2134} are {112233, 121233, 122133, 211233, 212133, 221133, 311223, 312123, 312213, 321123, 321213, 322113, 331122, 331212, 331221, 332112, 332121, 332211}

PROG

(PARI) a(n)=2*n^2+6*n-2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Sequence in context: A110671 A134078 A323148 * A301715 A269755 A270135

Adjacent sequences:  A181507 A181508 A181509 * A181511 A181512 A181513

KEYWORD

nonn,easy

AUTHOR

Lara Pudwell, Oct 25 2010

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)