login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A131804 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. 2
0, 0, -1, -1, 1, 2, 1, 2, 6, 8, 7, 9, 15, 18, 17, 20, 28, 32, 31, 35, 45, 50, 49, 54, 66, 72, 71, 77, 91, 98, 97, 104, 120, 128, 127, 135, 153, 162, 161, 170, 190, 200, 199, 209, 231, 242, 241, 252, 276, 288, 287, 299, 325, 338, 337, 350, 378, 392, 391, 405, 435, 450 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T is obtained by replacing the values of the second, fourth, sixth, ... column of the triangular array defined in A129819 by the corresponding negative values.

Interleaving of A000384, A001105, A056220 and A014107 (starting at the second term).

Main diagonal of T is in A001057, row sums are in A131805.

LINKS

Table of n, a(n) for n=0..61.

FORMULA

a(0) = 0, a(1) = 0, a(2) = -1, a(3) = -1, a(4) = 1, a(5) = 2, a(6) = 1; for n > 6, a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 7*a(n-4) + 5*a(n-5) - 3*a(n-6) + a(n-7);

G.f.: x^2*(-1+2*x-x^2+x^3)/((1-x)^3*(1+x^2)^2).

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:=62; 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] ];

(PARI) {for(n=0, 61, r=n%4; k=(n-r)/4; a=if(r==0, k*(2*k-1), if(r==1, 2*k^2, if(r==2, 2*k^2-1, k*(2*k+1)-1))); print1(a, ", "))}

CROSSREFS

Cf. A129819, A000384 (n*(2*n-1)), A001105 (2*n^2), A056220 (2*n^2-1), A014107 (n*(2*n-3)), A001057, A131805.

Sequence in context: A020825 A259992 A110422 * A254198 A246466 A170829

Adjacent sequences:  A131801 A131802 A131803 * A131805 A131806 A131807

KEYWORD

sign

AUTHOR

Klaus Brockhaus, Jul 18 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.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 07:50 EST 2018. Contains 299599 sequences. (Running on oeis4.)