

A116732


a(n) = a(n1) + a(n2) + a(n3)  a(n4).


5



0, 0, 0, 1, 1, 2, 4, 6, 11, 19, 32, 56, 96, 165, 285, 490, 844, 1454, 2503, 4311, 7424, 12784, 22016, 37913, 65289, 112434, 193620, 333430, 574195, 988811, 1702816, 2932392, 5049824, 8696221, 14975621, 25789274, 44411292, 76479966, 131704911, 226806895
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OFFSET

0,6


COMMENTS

This sequence is an example of a "symmetric" quartic recurrence and has some expected divisibility properties.
a(n3) counts partially ordered partitions of (n3) into parts 1,2,3 where only the order of the adjacent 1's and 3's are unimportant (see example).  David Neil McGrath, Jul 25 2015


LINKS

Table of n, a(n) for n=0..39.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1).


FORMULA

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


EXAMPLE

Partially ordered partitions of (n3) into parts 1,2,3 where only the order of adjacent 1's and 3's are unimportant. E.g., a(n3)=a(6)=19. These are (33),(321),(312),(231),(123),(132),(3111),(2211),(1122),(1221),(2112),(2121),(1212),(21111),(12111),(11211),(11121),(11112),(111111).  David Neil McGrath, Jul 25 2015


MATHEMATICA

LinearRecurrence[{1, 1, 1, 1}, {0, 0, 0, 1}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)


PROG

(PARI) v=[0, 0, 0, 1]; for(i=1, 40, v=concat(v, v[#v]+v[#v1]+v[#v2]v[#v3])); v \\ Derek Orr, Aug 27 2015


CROSSREFS

Close to A000786 (& A048239), A115992, A115993. Cf. A116201.
Sequence in context: A115992 A115993 A136424 * A048239 A000786 A000694
Adjacent sequences: A116729 A116730 A116731 * A116733 A116734 A116735


KEYWORD

nonn,easy


AUTHOR

R. K. Guy, Mar 23 2008


EXTENSIONS

More terms from Max Alekseyev, Mar 23 2008


STATUS

approved



