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A172176 Triangle t(n,m) = 1 + (n+m-n*m) *(2n-m-n(n - m)) read by rows, 0<=m<=n. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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...

LINKS

Table of n, a(n) for n=0..55.

FORMULA

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).

EXAMPLE

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;

MAPLE

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) ;

MATHEMATICA

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[%]

CROSSREFS

Sequence in context: A030768 A051480 A071572 * A143537 A125916 A100244

Adjacent sequences:  A172173 A172174 A172175 * A172177 A172178 A172179

KEYWORD

sign,tabl,easy

AUTHOR

Roger L. Bagula, Jan 28 2010

STATUS

approved

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Last modified December 8 21:00 EST 2016. Contains 278950 sequences.