A229035 Partial sums of A082233 (read sequentially meandering).

1, 3, 6, 11, 15, 18, 22, 27, 33, 40, 49, 57, 64, 70, 75, 81, 88, 96, 105, 115, 126, 139, 151, 162, 172, 181, 189, 196, 204, 213, 223, 234, 246, 259, 273, 288, 305, 321, 336, 350, 363, 375, 386, 396, 405, 415, 426, 438, 451, 465, 480, 496

Offset

1,2

Links

Table of n, a(n) for n=1..52.

Example

A082233 begins:
1,2,3,4,5,6,7,8,9,10
3,4,5,6,7,8,9,10,11,12
5,6,7,8,9,10,11,12,13,14
so this sequence begins 1, 1+2, 1+2+3, 1+2+3+5, 1+2+3+5+4, etc...

Maple

r:=0 ;
c:=1 ;
A082233 := proc(n, k)
    2*n+k ;
end proc:
A229035 := proc(n)
    option remember;
    global r, c ;
    local d;
    if n = 0 then
        A082233(r, c) ;
    else
        d := r+c ;
        if type(d, 'odd') then
            c := c+1 ;
            r := r-1 ;
            if r < 0 then
                r :=0 ;
            end if;
        else
            c := c-1 ;
            r := r+1 ;
            if c < 1 then
                c :=1 ;
            end if;
        end if;
        procname(n-1)+A082233(r, c) ;
    end if;
end proc: # R. J. Mathar, Sep 21 2013

Prog

(JavaScript)
a=new Array();
for (i=0; i<10; i++) {
a[i]=new Array();
for (j=0; j<10; j++) a[i][j]=1+2*i+j;
}
for (i=0; i<10; i++) document.write(a[i]+'<br>');
document.write('<br>');
xp=0; yp=0; d=0; s=1;
document.write(s+", ");
for (i=0; i<4; i++) {
if (d==0) {xp++; d=1; s+=a[yp][xp]; document.write(s+", "); }
if (d==1) {while (xp>0) {xp--; yp++; s+=a[yp][xp]; document.write(s+", "); }; d=2; }
if (d==2) {yp++; d=3; s+=a[yp][xp]; document.write(s+", "); }
if (d==3) {while (yp>0) {xp++; yp--; s+=a[yp][xp]; document.write(s+", "); }; d=0; }
}

Crossrefs

Cf. A082233.

Sequence in context: A310098 A310099 A056232 * A187896 A225521 A067278

Adjacent sequences: A229032 A229033 A229034 * A229036 A229037 A229038

Keyword

nonn

Author

Jon Perry, Sep 11 2013

Status

approved