0,2

Row sums of Riordan array (1/(1-x), x(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Feb 16 2005

a(n)=number of partitions of {1,...,n+3} into two blocks in which only 1- or 3-strings of consecutive integers can appear in a block and there is at least one 3-string. E.g. a(3)=5 because the enumerated partitions of {1,2,3,4,5,6} are 1235/46, 1345/26,15/2346,13/2456,123/456. - A. O. Munagi (amunagi(AT)yahoo.com), Apr 11 2005

A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463

A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005), 451-463.

Partial sums of A000930. a(n-1)=sum{k=0..floor(n/2), binomial(n-2k, k+1)}. - Paul Barry (pbarry(AT)wit.ie), Jul 07 2004

a(n-3)=Sum(binomial(n-r, r)), r=1, 2, ... which is the case t=3 and k=2 in the general case of t-strings and k blocks: a(n-3, k, t) = Sum(binomial(n-r*(t-1), r)*S2(n-r*(t-1)-1, k-1)), r=1, 2, ... - A. O. Munagi (amunagi(AT)yahoo.com), Apr 11 2005

a:= n-> (Matrix(4, (i, j)-> if i=j-1 then 1 elif j=1 then [2, -1, 1, -1][i] else 0 fi)^n)[1, 1]: seq (a(n), n=0..41); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008]

g:=(1+z+z^2)/(1-z-z^3): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-1, n=1..42); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]

Cf. A077941.

Cf. A105489, A000071.

Sequence in context: A014605 A132842 A063978 this_sequence A109537 A081226 A156623

Adjacent sequences: A077865 A077866 A077867 this_sequence A077869 A077870 A077871

nonn

N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002

More terms from A. O. Munagi (amunagi(AT)yahoo.com), Apr 11 2005