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A176286 Triangle t(n,k) = 1 +2*k*(n-k)*(k^2-n*k+2*n^2) read by rows, 0<=k<=n. 0
1, 1, 1, 1, 15, 1, 1, 65, 65, 1, 1, 175, 225, 175, 1, 1, 369, 529, 529, 369, 1, 1, 671, 1025, 1135, 1025, 671, 1, 1, 1105, 1761, 2065, 2065, 1761, 1105, 1, 1, 1695, 2785, 3391, 3585, 3391, 2785, 1695, 1, 1, 2465, 4145, 5185, 5681, 5681, 5185, 4145, 2465, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

This could be written t(n,k) = 1-(n-k)^4 -k^4 +n^4, the quartic analog of A176284.

Row sums are 1, 2, 17, 132, 577, 1798, 4529, 9864, 19329, 34954, 59345,... = (n+1)*(9*n^4 -9*n^3 -n^2 +n +15)/15.

LINKS

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

FORMULA

t(n,k) = t(n,n-k).

EXAMPLE

1;

1, 1;

1, 15, 1;

1, 65, 65, 1;

1, 175, 225, 175, 1;

1, 369, 529, 529, 369, 1;

1, 671, 1025, 1135, 1025, 671, 1;

1, 1105, 1761, 2065, 2065, 1761, 1105, 1;

1, 1695, 2785, 3391, 3585, 3391, 2785, 1695, 1;

1, 2465, 4145, 5185, 5681, 5681, 5185, 4145, 2465, 1;

1, 3439, 5889, 7519, 8449, 8751, 8449, 7519, 5889, 3439, 1;

MATHEMATICA

f[n_, m_, q_] := f[n, m, q] = 1 - ((n - m)^q + m^q - n^q);

Table[Flatten[Table[Table[f[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

CROSSREFS

Sequence in context: A040225 A070644 A174389 * A111805 A238754 A176226

Adjacent sequences:  A176283 A176284 A176285 * A176287 A176288 A176289

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Apr 14 2010

EXTENSIONS

Edited by R. J. Mathar, May 03 2013

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)