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A172176
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Triangle t(n,m) = 1 + (n+m-n*m) *(2n-m-n(n - m)) read by rows, 0<=m<=n.
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1
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1, 2, 2, 1, 2, 1, -8, 0, 0, -8, -31, -4, 5, -4, -31, -74, -10, 22, 22, -10, -74, -143, -18, 57, 82, 57, -18, -143, -244, -28, 116, 188, 188, 116, -28, -244, -383, -40, 205, 352, 401, 352, 205, -40, -383, -566, -54, 330, 586, 714, 714, 586, 330, -54, -566, -799
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history;
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OFFSET
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0,2
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COMMENTS
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Row sums are (n+1)*(n^4-9*n^3+15*n^2-n+6)/6 = 1, 4, 4, -16, -65, -124, -126, 64, 669, 2020, 4576...
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LINKS
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Table of n, a(n) for n=0..55.
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FORMULA
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t(n,m) = t(n,n-m).
t(n,0) = 1-A027620(n-3).
t(n,1) = -A028552(n-3).
t(n,2) = A033445(n-2).
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EXAMPLE
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1;
2, 2;
1, 2, 1;
-8, 0, 0, -8;
-31, -4, 5, -4, -31;
-74, -10, 22, 22, -10, -74;
-143, -18, 57, 82, 57, -18, -143;
-244, -28, 116, 188, 188, 116, -28, -244;
-383, -40, 205, 352, 401, 352, 205, -40, -383;
-566, -54, 330, 586, 714, 714, 586, 330, -54, -566;
-799, -70, 497, 902, 1145, 1226, 1145, 902, 497, -70, -799;
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MAPLE
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A172176 := proc(n, m) 1+(n+m-n*m)*(2*n-m-n*(n-m)) ; end proc:
seq(seq(A172176(n, m), m=0..n), n=0..10) ;
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MATHEMATICA
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Clear[t, n, m];
t[n_, m_] = 1 + (n + m - n*m)*(n + (n - m) - n(n - m));
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A030768 A051480 A071572 * A125916 A143537 A100244
Adjacent sequences: A172173 A172174 A172175 * A172177 A172178 A172179
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KEYWORD
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sign,tabl,easy
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AUTHOR
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Roger L. Bagula, Jan 28 2010
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STATUS
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approved
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