0,3

Floor[ arithmetic mean of next n numbers]. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 11 2003

Pairwise sums of repeated squares (A008794).

Also, number of topologies on n+1 unlabeled elements with exactly 4 elements in the topology. a(3) gives 4 elements a,b,c,d; the valid topologies are (0,a,ab,abcd), (0,a,abc,abcd), (0,ab,abc,abcd), (0,a,bcd,abcd) and (0,ab,cd,abcd), with a count of 5. - Jon Perry (perry(AT)globalnet.co.uk), Mar 05 2004

Euler transform of a(n+1) is length 4 sequence [2,2,0,-1].

Partition n in two parts, say r and s so that r^2 + s^2 is minimal, then a(n) = r^2 +s^2. Geometrical significance: folding a rod with length n units at right angles in such a way that the end points are at the least distance, which is given by a(n)^(1/2) as the hypotenus of a right angled triangle with the sum of the base and height = n units. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 18 2004

Convolution of A002061(n)-0^n and (-1)^n. Convolution of n (A001477) with {1,0,2,0,2,0,2...}. Partial sums of repeated odd numbers {0,1,1,3,3,5,5,...}. - Paul Barry (pbarry(AT)wit.ie), Jul 22 2004

The ratio of the sum of terms over the total number of terms in an n X n spiral. The sum of terms of an n X n spiral is A037270, or Sum{k=0..n^2,k} = (n^4 + n^2)/2 and the total number of terms is n^2. - William A. Tedeschi (fynmun(AT)hotmail.com), Feb 27 2008

Starting with offset 1 = row sums of triangle A158946. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 31 2009]

Partial sums of A109613. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 05 2009]

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

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.

S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta and K.M. Tamizhmani, Blending two discrete integrability criteria: ...

MathWorld, Topology

a(2n) = 2n^2, a(2n+1) = 2n^2 + 2n + 1.

a(n) = (2n^2 + 1 - (-1)^n) / 4. a(0)=0, a(1)=1, a(n+1)=n+1+max(2*floor(a(n)/2); 3*floor(a(n)/3)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 06 2002

G.f.: (x+x^2+x^3+x^4)/((1-x)*(1-x^2)^2) - Len Smiley (smiley(AT)math.uaa.alaska.edu).

a(n)=a(n-2)+2n-2. - Paul Barry (pbarry(AT)wit.ie), Jul 17 2004

G.f.: x(1+x^2)/((1-x^2)(1-x)^2)=x(1+x^2)/((1+x)(1-x)^3); a(n)=sum{k=0..n, (k^2-k+1-0^k)(-1)^(n-k) }; a(n)=sum{k=0..n, ((1+(-1)^(n-k))-0^(n-k))k }. - Paul Barry (pbarry(AT)wit.ie), Jul 22 2004

a(0) = 0, a(n+1) = a(n) + 2*floor(n/2) + 1. a(n) = A116940(n) - A005843(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2006

Starting with offset 1, = row sums of triangle A134444. Also, with offset 1, = binomial transform of [1, 1, 2, -2, 4, -8, 16, -32,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 25 2007

a(n) = floor((n^2+1)/2) - William A. Tedeschi (fynmun(AT)hotmail.com), Feb 27 2008

Contribution from Yosu Yurramendi (yosu.yurramendi(AT)ehu.es), Sep 12 2008: (Start)

a(n) = A004526(n+2) + A000217 (n)

(End)

Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 05 2008: (Start)

a(n)=a(n-1)+a(n-2)-a(n-3)+2

a(n)=2a(n-1)-2a(n-3)+a(n-4) (End)

a(n)=A004526(n)^2 + A110654(n)^2. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 12 2009]

A000982:=-(1+z**2)/(z+1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]

with (combinat):seq(count(Partition((n^2+1)), size=2), n=0..53); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2008

Cf. A000096.

Cf. A134444.

Cf. A037270.

A158946 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 31 2009]

Sequence in context: A076145 A049617 A054074 this_sequence A122221 A083704 A111097

Adjacent sequences: A000979 A000980 A000981 this_sequence A000983 A000984 A000985

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com).