OFFSET
0,5
COMMENTS
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(0) = 0; a(n) = a(n-1) - (n mod 2) + n*(1 - (n mod 2)) for n > 0.
G.f.: x*(-1+2*x+x^2)/((1-x)^3*(1+x)^2).
a(n) = -A131118(2n) = (2n(n-1)+(2n+3)(-1)^n-3)/8. - Bruno Berselli, Mar 27 2012
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]: k in [1..j] ]: j in [1..m] ];
(Magma) m:=29; &cat[ [ n^2, n^2-1 ]: n in [0..m] ];
(PARI) {m=58; for(n=0, m, r=n%2; print1(((n-r)/2)^2-r, ", "))}
(Maxima) makelist((2*n*(n-1)+(2*n+3)*(-1)^n-3)/8, n, 0, 58); /* Bruno Berselli, Mar 27 2012 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Klaus Brockhaus, Jul 18 2007
STATUS
approved