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A178304
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Triangle T(n,m) = 1 + f(n+1)*(f(m+1) + f(n-m+1) - 1 - f(n+1)), read by rows, where f(.)=A002487(.).
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1
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1, 1, 1, 1, -1, 1, 1, 2, 2, 1, 1, -5, 1, -5, 1, 1, 3, 1, 1, 3, 1, 1, -2, 4, -5, 4, -2, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, -11, 1, -7, 5, -7, 1, -11, 1, 1, 4, -2, 1, 4, 4, 1, -2, 4, 1, 1, -9, 1, -19, 1, -9, 1, -19, 1, -9, 1
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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Row sums are 1, 2, 1, 6, -7, 10, 1, 20, -27, 16, -59, ...
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LINKS
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Table of n, a(n) for n=0..65.
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EXAMPLE
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Rows n >= 0, 0 <= k <= n begin
1;
1, 1;
1, -1, 1;
1, 2, 2, 1;
1, -5, 1, -5, 1;
1, 3, 1, 1, 3, 1;
1, -2, 4, -5, 4, -2, 1;
1, 3, 3, 3, 3, 3, 3, 1;
1, -11, 1, -7, 5, -7, 1, -11, 1;
1, 4, -2, 1, 4, 4, 1, -2, 4, 1;
1, -9, 1, -19, 1, -9, 1, -19, 1, -9, 1;
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MAPLE
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A002487 := proc(n) option remember; if n <=1 then n; else if type(n, 'even') then procname(n/2) ; else procname((n-1)/2)+procname(1+(n-1)/2) ; end if; end if; end proc:
A178304 := proc(n, m) 1 + A002487(n+1)*( A002487(m+1)+A002487(n-m+1)-1-A002487(n+1) ) ; end proc:
seq(seq(A178304(n, k), k=0..n), n=0..15) ; # N. J. A. Sloane, Jul 20 2010
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MATHEMATICA
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a[0] = 0; a[1] = 1;
a[n_] := a[n] = If[Mod[n, 2] == 0, a[Floor[n/2]], a[ Floor[(n - 1)/2]] + a[Floor[(n + 1)/2]]];
tg[n_, m_] := 1 + a[n + 1]*a[m + 1] + a[n + 1]*a[n - m + 1] - (a[n + 1]*a[ 0 + 1] + a[n + 1]*a[n - 0 + 1]);
Table[Table[tg[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Cf. A002487, A177443.
Sequence in context: A209543 A178655 A337278 * A123585 A145668 A318405
Adjacent sequences: A178301 A178302 A178303 * A178305 A178306 A178307
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KEYWORD
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sign,tabl,easy
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, May 24 2010
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EXTENSIONS
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Definition simplified by the Assoc. Eds. of the OEIS, Jul 20 2010
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STATUS
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approved
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