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

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, ... - njas, 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.

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)