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A167613
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Array T(n,k) read by antidiagonals: the k-th term of the n-th difference of A131531.
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4
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0, 0, 0, 1, 1, 1, 0, -1, -2, -3, 0, 0, 1, 3, 6, -1, -1, -1, -2, -5, -11, 0, 1, 2, 3, 5, 10, 21, 0, 0, -1, -3, -6, -11, -21, -42, 1, 1, 1, 2, 5, 11, 22, 43, 85, 0, -1, -2, -3, -5, -10, -21, -43, -86, -171, 0, 0, 1, 3, 6, 11, 21, 42, 85, 171, 342, -1, -1, -1, -2, -5, -11, -22, -43, -85, -170, -341, -683, 0, 1, 2, 3, 5, 10, 21, 43, 86, 171, 341, 682, 1365
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refs;
listen;
history;
text;
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OFFSET
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0,9
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COMMENTS
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LINKS
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FORMULA
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T(0,k) = A131531(k). T(n,k) = T(n-1,k+1) - T(n-1,k), n > 0.
T(n,0) = -T(n,3) = (-1)^(n+1)*A024495(n).
T(n,k+6) = T(n,k).
a(n) = A131708(0), -A024495(0,1), A024493(0,1,2), -A131708(0,1,2,3), A024495(0,1,2,3,4), -A024493(0,1,2,3,4,5).
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EXAMPLE
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The table starts in row n=0 with columns k >= 0 as:
0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0 A131531
0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1 A092220
1, -2, 1, -1, 2, -1, 1, -2, 1, -1, 2, -1, 1, -2, 1, -1, 2, -1, 1, -2 A131556
-3, 3, -2, 3, -3, 2, -3, 3, -2, 3, -3, 2, -3, 3, -2, 3, -3, 2, -3 A164359
6, -5, 5, -6, 5, -5, 6, -5, 5, -6, 5, -5, 6, -5, 5, -6, 5, -5, 6, -5
-11, 10, -11, 11, -10, 11, -11, 10, -11, 11, -10, 11, -11, 10, -11
21, -21, 22, -21, 21, -22, 21, -21, 22, -21, 21, -22, 21, -21, 22
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MAPLE
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A131531 := proc(n) op((n mod 6)+1, [0, 0, 1, 0, 0, -1]) ; end proc:
A167613 := proc(n, k) option remember; if n= 0 then A131531(k); else procname(n-1, k+1)-procname(n-1, k) ; end if; end proc: # R. J. Mathar, Dec 17 2010
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MATHEMATICA
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nmax = 13;
A131531 = Table[{0, 0, 1, 0, 0, -1}, {nmax}] // Flatten;
T[n_] := T[n] = Differences[A131531, n];
T[n_, k_] := T[n][[k]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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