0,2

Same as Pisot sequences E(1,4), L(1,4), P(1,4), T(1,4). See A008776 for definitions of Pisot sequences.

The convolution square root of this sequence is A000984, the central binomial coefficients: C(2n,n). - T. D. Noe (noe(AT)sspectra.com), Jun 11 2002

a(n)=sum(k=0,n,C(2k,k)*C(2(n-k),n-k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003

With p(n) = the number of integer partitions of n, p(i) = the number of parts of the i-th partition of n, d(i) = the number of different parts of the i-th partition of n, m(i,j) = multiplicity of the j-th part of the i-th partition of n, sum_{i=1}^{p(n)} = sum over i, and prod_{j=1}^{d(i)} = product over j one has: a(n)=sum_{i=1}^{p(n)} p(i)!/(prod_{j=1}^{d(i)} m(i,j)!) * 2^(n-1) - Thomas Wieder (wieder.thomas(AT)t-online.de), May 18 2005

Sums of rows of the triangle in A122366. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 30 2006

A000005(a(n)) = A005408(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

T. D. Noe, Table of n, a(n) for n = 0..100

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Tanya Khovanova, Recursive Sequences

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 8

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 269

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Eric Weisstein's World of Mathematics, Cantor Dust

Index entries for "core" sequences

a(n) = 4^n; a(n) = 4a(n-1).

G.f.: 1/(1-4x), e.g.f.: exp(4x)

1 = Sum(n = 1 through infinity) 3/a(n) = 3/4 + 3/16 + 3/64 + 3/256 + 3/1024...; with partial sums: 3/4, 15/16, 63/64, 255/256, 1023/1024... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 16 2003

a(n)=A001045(2n)+A001045(2n+1). - Paul Barry (pbarry(AT)wit.ie), Apr 27 2004

a(n)=sum(2^(n-j)*binomial(n+j,j),j=0..n) - Peter C. Heinig (algorithms(AT)gmx.de), Apr 06 2007

Hankel transform of A115967 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 22 2007

A000302 := n->4^n;

for n from 1 to 10 do sum(2^(n-j)*binomial(n+j, j), j=0..n); od; - Peter C. Heinig (algorithms(AT)gmx.de), Apr 06 2007

A000302:=-1/(-1+4*z); [Conjectured by S. Plouffe in his 1992 dissertation.]

Table[4^n, {n, 0, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 01 2006

Cf. A024036, A052539.

Adjacent sequences: A000299 A000300 A000301 this_sequence A000303 A000304 A000305

Sequence in context: A006811 A005755 A077821 this_sequence A050734 A075614 A083592

easy,nonn,nice,core

njas