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A125166 Triangle, companion to A125165, left border = n^3. 0
1, 8, 1, 27, 9, 1, 64, 36, 10, 1, 125, 100, 46, 11, 1, 216, 225, 146, 57, 12, 1, 343, 441, 371, 203, 69, 13, 1512, 784, 812, 574, 272, 82, 14, 1, 729, 1296, 1596, 1386, 846, 354, 96, 15, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Column next to left border = (1, 9, 36, 100, 225...) squares of triangular numbers. A125165 uses analogous operations with n^2 on the left border instead of n^3. Row sums = 1, 9, 37, 111, 283, 657...a sequence analogous to row sums for A125165; i.e. A050488: (1, 5, 15, 37, 83, 177...).

Riordan array ((1+4*x+x^2)/(1-x)^4, x/(1-x)). - Philippe Deléham, Dec 09 2013

LINKS

Table of n, a(n) for n=0..43.

FORMULA

Binomial transform of an infinite matrix M with diagonal D, subdiagonal (D-1)..., etc; as follows: (D) = (1,1,1...); (D-1) = (7,7,7...); (D-2) = (12,12,12...); (D-3) = (6,6,6...). Alternatively, given left border n^3: (1, 8, 27, 64...); for k>1, T(n,k) = (n-1,k) + (n-1,k-1).

EXAMPLE

(5,3) = 146 = (4,3) + (4,2) = 46 + 100. First few rows of the triangle are:

1;

8, 1;

27, 9, 1;

64, 36, 10, 1;

125, 100, 46, 11, 1;

216, 225, 146, 57, 12, 1;

343, 441, 371, 203, 69, 13, 1;

512, 784, 812, 574, 272, 82, 14, 1;

...

CROSSREFS

Cf. A000578, A125165, A050488.

Sequence in context: A138505 A002173 A050458 * A211785 A075155 A075151

Adjacent sequences:  A125163 A125164 A125165 * A125167 A125168 A125169

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 22 2006

STATUS

approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)