0,3

Powers of 2 doubled up. The usual OEIS policy is to omit the duplicates in such cases (when this would become A000079). This is an exception.

Number of symmetric partitions of n: e.g. 5 = 2+1+2 = 1+3+1 = 1+1+1+1+1 so a(5) = 4; 6 = 3+3 = 2+2+2 = 1+4+1 = 2+1+1+2 = 1+2+2+1 = 1+1+2+1+1 = 1+1+1+1+1+1 so a(6) = 8. - Henry Bottomley (se16(AT)btinternet.com), Dec 10 2001

Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.

E. Deutsch, Problem 1633, Math. Mag., 74 #5 (2001), p. 403.

D. Merlini, F. Uncini and M. C. Verri, A unified approach to the study of general and palindromic compositions, Integers 4 (2004), A23, 26 pp.

S. Heubach and T. Mansour, Counting rises, levels, and drops in compositions

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1067

a(n) = a(n-1)*a(n-2)/a(n-3) = 2a(n-2) = 2^A004526(n). G.f.: (1+x)/(1-2x^2)

(1/2+sqrt(1/8))*sqrt(2)^n+(1/2-sqrt(1/8))*(-sqrt(2))^n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 11 2003

E.g.f.: cosh(sqrt(2)x)+sinh(sqrt(2)x)/sqrt(2). - Paul Barry (pbarry(AT)wit.ie), Jul 16 2003

The signed sequence (-1)^n2^[n/2] has a(n)=(sqrt(2))^n(1/2-sqrt(2)/4)+(-sqrt(2))^n(1/2+sqrt(2)/4). It is the inverse binomial transform of A000129(n-1). - Paul Barry (pbarry(AT)wit.ie), Apr 21 2004

Diagonal sums of A046854. a(n)=sum{k=0..n, binomial(floor(n/2), k)}. - Paul Barry (pbarry(AT)wit.ie), Jul 07 2004

a(n)=a(n-2)+2^floor((n-2)/2) - Paul Barry (pbarry(AT)wit.ie), Jul 14 2004

a(n)=sum{k=0..floor(n/2), binomial(floor(n/2), floor(k/2)) } - Paul Barry (pbarry(AT)wit.ie), Jul 15 2004

E.g.f.: cosh(asinh(1)+sqrt(2)*x)/sqrt(2). - Michael Somos Feb 28 2005

a(n)= Sum_{k, 0<=k<=n}A103633(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2006

seq(mul(mul(j, j=1..2), k=1..n/2), n=0..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 21 2007

Table[ 2^Floor[n/2], {n, 0, 42}] (from Robert G. Wilson v Jun 05 2004)

(PARI) a(n)=if(n<0, 0, 2^(n\2))

Cf. A006995, A057148.

Cf. A112030, A112033.

a(n) = A094718(3, n).

Adjacent sequences: A016113 A016114 A016115 this_sequence A016117 A016118 A016119

Sequence in context: A076939 A131572 A117575 this_sequence A060546 A120803 A000011

nonn

njas