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A275490
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Square array of 5D pyramidal numbers, read by antidiagonals.
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2
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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
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OFFSET
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2,3
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COMMENTS
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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).
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LINKS
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FORMULA
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A(n+2,k) = Sum_{j=0..k-1} A080852(n,j).
A(n,k) = binomial(k+3,4) + (n-2)*binomial(k+3,5). - Mathew Englander, Oct 27 2020
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EXAMPLE
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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
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MATHEMATICA
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Table[Binomial[k + 3, 4] + (# - 2)*Binomial[k + 3, 5] &[m - k + 1], {m, 2, 12}, {k, m - 1}] // Flatten (* Michael De Vlieger, Nov 05 2020 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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