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A275490 Square array of 5D pyramidal numbers, read by antidiagonals. 1
1, 1, 5, 1, 6, 15, 1, 7, 21, 35, 1, 8, 27, 56, 70, 1, 9, 33, 77, 126, 126, 1, 10, 39, 98, 182, 252, 210, 1, 11, 45, 119, 238, 378, 462, 330, 1, 12, 51, 140, 294, 504, 714, 792, 495, 1, 13, 57, 161, 350, 630, 966, 1254, 1287, 715, 1, 14, 63, 182, 406, 756, 1218, 1716, 2079, 2002, 1001 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Let F(r,n,d) = binomial(r+d-2,d-1)* ((r-1)*(n-2)+d) /d  be the d-dimensional pyramidal numbers. Then A(n,k) = F(k,n,5).

LINKS

Table of n, a(n) for n=2..67.

Index to sequences related to polygonal numbers

FORMULA

A(n+2,k) = Sum_{j=0..k-1} A080852(n,j).

EXAMPLE

The array starts in rows n>=2 and columns k>=1 as

   1    5   15   35   70  126  210  330  495   715  1001  1365  1820

   1    6   21   56  126  252  462  792 1287  2002  3003  4368  6188

   1    7   27   77  182  378  714 1254 2079  3289  5005  7371 10556

   1    8   33   98  238  504  966 1716 2871  4576  7007 10374 14924

   1    9   39  119  294  630 1218 2178 3663  5863  9009 13377 19292

   1   10   45  140  350  756 1470 2640 4455  7150 11011 16380 23660

   1   11   51  161  406  882 1722 3102 5247  8437 13013 19383 28028

   1   12   57  182  462 1008 1974 3564 6039  9724 15015 22386 32396

   1   13   63  203  518 1134 2226 4026 6831 11011 17017 25389 36764

CROSSREFS

Cf. Row sums of A080852 (4D), A080851 (3D), A057145 (2D), A077028 (1D).

Sequence in context: A007397 A204203 A261721 * A052345 A197733 A241018

Adjacent sequences:  A275487 A275488 A275489 * A275491 A275492 A275493

KEYWORD

nonn,easy,tabl

AUTHOR

R. J. Mathar, Jul 30 2016

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)