This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A129819 Antidiagonal sums of triangular array T: T(j,k) = (k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j. 7
 0, 0, 1, 1, 3, 4, 7, 8, 12, 14, 19, 21, 27, 30, 37, 40, 48, 52, 61, 65, 75, 80, 91, 96, 108, 114, 127, 133, 147, 154, 169, 176, 192, 200, 217, 225, 243, 252, 271, 280, 300, 310, 331, 341, 363, 374, 397, 408, 432, 444, 469, 481, 507, 520, 547, 560, 588, 602, 631 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Interleaving of A077043 and A006578. First differences are in A124072. If the values of the second, fourth, sixth, ... column are replaced by the corresponding negative values, the antidiagonal sums of the resulting triangular array are 0, 0, 1, 1, -1, -2, -1, -2, -6, -8, -7, -9, ... . Row sums of triangle A168316 = (1, 1, 3, 4, 7, 8, 12, ...). - Gary W. Adamson, Nov 22 2009 LINKS FORMULA a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7) for n > 6, with a(0) = 0, a(1) = 0, a(2) = 1, a(3) = 1, a(4) = 3, a(5) = 4, a(6) = 7. G.f.: x^2*(1+x^2+x^3)/((1-x)^3*(1+x)^2*(1+x^2)). a(n) = (3/16)*(n+2)*(n+1) - (5/8)*(n+1) + 7/32 + (3/32)*(-1)^n + (1/16)*(n+1)*(-1)^n - (1/8)*cos(n*Pi/2) + (1/8)*sin(n*Pi/2). - Richard Choulet, Nov 27 2008 EXAMPLE First seven rows of T are [ 0 ] [ 0, 1 ] [ 0, 1, 2 ] [ 0, 1, 3, 2 ] [ 0, 1, 4, 2, 3 ] [ 0, 1, 5, 2, 4, 3 ] [ 0, 1, 6, 2, 5, 3, 4 ]. PROG (MAGMA) m:=59; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do for k:=2 to j do if k mod 2 eq 0 then M[j, k]:= k div 2; else M[j, k]:=j-(k div 2); end if; end for; end for; [ &+[ M[j-k+1, k]: k in [1..(j+1) div 2] ]: j in [1..m] ]; // Klaus Brockhaus, Jul 16 2007 (PARI) {vector(59, n, (n-2+n%2)*(n+n%2)/8+floor((n-2-n%2)^2/16))} // Klaus Brockhaus, Jul 16 2007 CROSSREFS Cf. A077043, A006578, A124072. Cf. A168316. - Gary W. Adamson, Nov 22 2009 Sequence in context: A282166 A165157 A182079 * A025032 A207524 A003141 Adjacent sequences:  A129816 A129817 A129818 * A129820 A129821 A129822 KEYWORD nonn AUTHOR Paul Curtz, May 20 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, Jul 16 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 16 02:45 EDT 2018. Contains 316252 sequences. (Running on oeis4.)