A275490 - OEIS

A275490

Square array of 5D pyramidal numbers, read by antidiagonals.

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

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).

Sum of the n-th antidiagonal is binomial(n+4,7) + binomial(n+4,5) = A055797(n-1). - Mathew Englander, Oct 27 2020

LINKS

Michael De Vlieger, Table of n, a(n) for n = 2..11176 (rows 2 <= n <= 150, flattened)

Index to sequences related to polygonal numbers

FORMULA

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

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

MATHEMATICA

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 *)

CROSSREFS

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

Cf. A055797.

Sequence in context: A362489 A204203 A261721 * A052345 A197733 A353874

Adjacent sequences: A275487 A275488 A275489 * A275491 A275492 A275493

KEYWORD

nonn,easy,tabl

AUTHOR

R. J. Mathar, Jul 30 2016

STATUS

approved