0,2

Let M_n be the n X n matrix m_(i,j)=2+abs(i-j) then det(M_n)=(-1)^(n-1)*a(n-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 28 2002

a(n) = number of triangulations of a regular (n+3)-gon in which every triangle shares at least one side with the polygon itself. - David Callan (callan(AT)stat.wisc.edu), Mar 25 2004

Number of compositions of j+n, j>n and j the maximum part. E.g. a(4) is derived from the number of compositions of, for example: 54(2), 531(6), 522(3), 5211(12) and 51111(5) giving 2+6+3+12+5=28. - Jon Perry (perry(AT)globalnet.co.uk), Sep 13 2005

If X_1,X_2,...,X_n are 2-blocks of a (2n+2)-set X then, for n>=1, a(n+1) is the number of (n+1)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007

Equals row sums of triangle A152195 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]

Generated from iterates of M * [1,1,1,...], where M = an infinite triadiagonal matrix with (1,1,1,...) in the main and superdiagonals and (1,0,0,0,...) in the subdiagonal. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 04 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Index entries for sequences related to linear recurrences with constant coefficients

Milan Janjic, Two Enumerative Functions

F. Ellermann, Illustration of binomial transforms

Sum_{k = 0..n } (k+2)!*binomial(n,k) gives the sequence but with a different offset: 2, 5, 12, 28, 64, 144, 320, 704, 1536, ... - N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2008

Binomial transform of 1,1,2,2,3,3,.... - Paul Barry (pbarry(AT)wit.ie), Mar 06 2003

a(0)=1, a(n)=(n+3)*2^(n-2), n >= 1. a(n+1) = 2*a(n) + 2^(n-1), n>0.

G.f.: (1-x)^2/((1-2*x)^2). Detlef Pauly (dettodet(AT)yahoo.de), Mar 03 2003

G.f.: 1/(1-x-x^2-x^3-...)^2 - Jon Perry (perry(AT)globalnet.co.uk), Jul 04 2004

a(n)=sum_{0<=i_1<=i_2<=n} binomial(n, i_1+i_2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 14 2004

a(n)= 2^(n-2)*(n+3) for n>0 - (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2005)

a(n)=Sum{k=0..n, C(n, k)*floor((k+2)/2)} - Paul Barry (pbarry(AT)wit.ie), Mar 06 2003

Equals row sums of A128254. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 20 2007

a(n+1)-2a(n)= 0, 1, 2, 4, 8, 16, ... = A131577 . - Paul Curtz (bpcrtz(AT)free.fr), May 18 2008

E.g. a(2)=5 because in the compositions of 3, namely 3,2+1,1+2,1+1+1, we have five 1's altogether.

seq(ceil(1/4*2^n*(n+3)), n=0..50);

Table[ If[n == 0, 1, 2^(n - 2)(n + 3)], {n, 0, 29}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2005)

(PARI) a(n)=if(n<1, n==0, (n+3)*2^(n-2))

Convolution of A011782.

A152195 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]

Sequence in context: A006979 A019301 A006980 this_sequence A001410 A019486 A019485

Adjacent sequences: A045620 A045621 A045622 this_sequence A045624 A045625 A045626

easy,nonn

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)