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A289692 The number of partitions of [n] with exactly 2 blocks without peaks. 2
0, 1, 2, 4, 8, 15, 27, 48, 85, 150, 264, 464, 815, 1431, 2512, 4409, 7738, 13580, 23832, 41823, 73395, 128800, 226029, 396654, 696080, 1221536, 2143647, 3761839, 6601568, 11584945 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..300

T. Mansour, M. Shattuck, Counting Peaks and Valleys in a Partition of a Set , J. Int. Seq. 13 (2010), 10.6.8, Table 1.

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-1).

FORMULA

From Colin Barker, Nov 07 2017: (Start)

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

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) for n>4. (End)

a(n) = A077855(n-2) - A005314(n-2) for n>1. - John Molokach, Jan 23 2018

MAPLE

a := proc(n) option remember: if n = 1 then 0 elif n = 2 then 1 elif n=3 then 2 elif n=4 then 4 elif  n >= 5 then 3*procname(n-1) -3*procname(n-2)+2*procname(n-3)-procname(n-4) fi; end:

seq(a(n), n = 0..100); # Muniru A Asiru, Jan 25 2018

MATHEMATICA

LinearRecurrence[{3, -3, 2, -1}, {0, 1, 2, 4}, 40] (* Vincenzo Librandi, Jan 26 2018 *)

PROG

(GAP) a:=[0, 1, 2, 4]; for n in [5..10^2] do a[n]:=3*a[n-1]-3*a[n-2]+2*a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Jan 25 2018

(MAGMA) I:=[0, 1, 2, 4]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jan 26 2018

CROSSREFS

Sequence in context: A182716 A143281 A098057 * A074029 A248729 A138653

Adjacent sequences:  A289689 A289690 A289691 * A289693 A289694 A289695

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jul 09 2017

STATUS

approved

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Last modified November 14 20:15 EST 2019. Contains 329130 sequences. (Running on oeis4.)