2,2

a(n-4) = number of n-th generation vertices in the tree of sequences with unit increase labeled by 5 (cf. Zoran Sunik reference) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 07 2003

Number of standard tableaux of shape (n+3,n-2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004

S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751

V. E. Hoggatt, Jr. and M. Bicknell, Catalan and related sequences arising from inverses of Pascal's triangle matrices, Fib. Quart., 14 (1976), 395-405.

J. Noonan, The number of permutations containing exactly one increasing subsequence of length three, Discrete Math. 152 (1996), no. 1-3, 307-313.

L. W. Shapiro, A Catalan triangle, Discrete Math. 14 (1976), no. 1, 83-90.

Zoran Sunik, Self describing sequences and the Catalan family tree, Elect. J. Combin., 10 (No. 1, 2003).

D. Callan, A recursive bijective approach to counting permutations...

R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6

J. Noonan and D. Zeilberger, [math/9808080] The Enumeration of Permutations With a Prescribed Number of ``Forbidden'' Patterns

6C(2n+1, n-2)/(n+4).

G.f.=x^2*C(x)^6, where C(x) is g.f. for the Catalan numbers (A000108). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004

E.g.f.: exp(2x)(Bessel_I(2,2x)-Bessel_I(4,2x)); - Paul Barry (pbarry(AT)wit.ie), Jun 04 2007

a(3)=6 because the only permutations of 1234 with exactly 1 increasing subsequence of length 3 are 1423, 4123, 1342, 2314, 2341, 3124.

T(n, n+6) for n=0, 1, 2, ..., array T as in A047072.

Cf. A001089, A084249.

First differences are in A026017.

A diagonal of any of the essentially equivalent arrays A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.

Cf. A000108 A000245 A002057 A000344 A003517 A000588 A003518 A003519 A001392.

Sequence in context: A037604 A022634 A094788 this_sequence A108958 A005284 A014825

Adjacent sequences: A003514 A003515 A003516 this_sequence A003518 A003519 A003520

nonn,easy,nice

njas