

A032091


Number of reversible strings with n1 beads of 2 colors. 4 beads are black. String is not palindromic.


6



2, 6, 16, 32, 60, 100, 160, 240, 350, 490, 672, 896, 1176, 1512, 1920, 2400, 2970, 3630, 4400, 5280, 6292, 7436, 8736, 10192, 11830, 13650, 15680, 17920, 20400, 23120, 26112, 29376, 32946, 36822, 41040, 45600, 50540, 55860
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

6,1


COMMENTS

Also, number of 4element subsets of the set {1,...,n1} whose elements sum up to an odd integer, i.e., 4th column of the triangle A159916, cf. there.  M. F. Hasler, May 01 2009
Also, if the offset is changed to 3, so that a(3)=2, a(n) = number of nonequivalent (mod D_3) ways to place 2 indistinguishable points on a triangular grid of side n so that they are not adjacent.  Heinrich Ludwig, Mar 23 2014


LINKS

Table of n, a(n) for n=6..43.
C. G. Bower, Transforms (2)
Elizabeth Wilmer, Notes on Stephan's conjectures 72, 73 and 74
Index to sequences with linear recurrences with constant coefficients, signature (3,1,5,5,1,3,1)


FORMULA

"BHK[ 5 ]" (reversible, identity, unlabeled, 5 parts) transform of 1, 1, 1, 1...
From M. F. Hasler, May 01 2009: (Start)
G.f.: 2 x^5 (1x)^5 (1+x)^2.
a(n) = [(n5)(n3)(n1)^2 + (6n15) X[2Z](n)]/48, where X[2Z] is the characteristic function of 2Z. (End)


PROG

From M. F. Hasler, May 01 2009: (Start)
(PARI) A032091(n)=polcoeff(2/(1x)^5/(1+x)^2+O(x^(n5)), n6)
A032091(n)=((n5)*(n3)*(n1)^2+if(n%2==0, 6*n15))/48 \\\\ (End)


CROSSREFS

a(n+6) = 2*A002624(n), A239572.
Sequence in context: A192735 A218212 A171218 * A182994 A235792 A192706
Adjacent sequences: A032088 A032089 A032090 * A032092 A032093 A032094


KEYWORD

nonn


AUTHOR

Christian G. Bower


STATUS

approved



