

A144204


Array A(k,n) = (n+k2)*(n1)  1 (k >= 1, n >= 1) read by antidiagonals.


0



1, 1, 0, 1, 1, 3, 1, 2, 5, 8, 1, 3, 7, 11, 15, 1, 4, 9, 14, 19, 24, 1, 5, 11, 17, 23, 29, 35, 1, 6, 13, 20, 27, 34, 41, 48, 1, 7, 15, 23, 31, 39, 47, 55, 63, 1, 8, 17, 26, 35, 44, 53, 62, 71, 80, 1, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 1, 10, 21, 32, 43, 54, 65, 76, 87
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OFFSET

1,6


COMMENTS

Arises in complete intersection threefolds,
Also can be produced as a triangle read by rows: a(n, k) = nk  (n + k).  Alonso del Arte, Jul 09 2009
Kosta: Let X be a complete intersection of two hypersurfaces F_n and F_k in the projective space P^5 of degree n and k respectively. with n=>k, such that the singularities of X are nodal and F_k is smooth. We prove that if the threefold X has at most (n+k2)*(n1)  1 singular points, then it is factorial.


LINKS

Table of n, a(n) for n=1..75.
Dimitra Kosta, Factoriality of complete intersection threefolds arXiv:0808.4071 [math.AG]


FORMULA

A[k,n] = (n+k2)*(n1)  1.
Antidiagonal sum: Sum_{n=1..d} A(dn+1,n) = d*(d^22d1)/2 = A110427(d).  R. J. Mathar, Jul 10 2009


EXAMPLE

From R. J. Mathar, Jul 10 2009: (Start)
The rows A(n,1), A(n,2), A(n,3), etc., are :
.1...0...3...8..15..24..35..48..63..80..99.120.143.168 A067998
.1...1...5..11..19..29..41..55..71..89.109.131.155.181 A028387
.1...2...7..14..23..34..47..62..79..98.119.142.167.194 A008865
.1...3...9..17..27..39..53..69..87.107.129.153.179.207 A014209
.1...4..11..20..31..44..59..76..95.116.139.164.191.220 A028875
.1...5..13..23..35..49..65..83.103.125.149.175.203.233 A108195
.1...6..15..26..39..54..71..90.111.134.159.186.215.246
.1...7..17..29..43..59..77..97.119.143.169.197.227.259
.1...8..19..32..47..64..83.104.127.152.179.208.239.272
.1...9..21..35..51..69..89.111.135.161.189.219.251.285
.1..10..23..38..55..74..95.118.143.170.199.230.263.298
.1..11..25..41..59..79.101.125.151.179.209.241.275.311
.1..12..27..44..63..84.107.132.159.188.219.252.287.324
.1..13..29..47..67..89.113.139.167.197.229.263.299.337 Cf. A126719.
(End)
As a triangle:
. 0
. 1, 3
. 2, 5, 8
. 3, 7, 11, 15
. 4, 9, 14, 19, 24
. 5, 11, 17, 23, 29, 35
. 6, 13, 20, 27, 34, 41, 48
. 7, 15, 23, 31, 39, 47, 55, 63
. 8, 17, 26, 35, 44, 53, 62, 71, 80


MAPLE

A := proc(k, n) (n+k2)*(n1)1 ; end: for d from 1 to 13 do for n from 1 to d do printf("%d, ", A(dn+1, n)) ; od: od: # R. J. Mathar, Jul 10 2009


MATHEMATICA

a[n_, k_] := a[n, k] = n*k  (n + k); ColumnForm[Table[a[n, k], {n, 10}, {k, n}], Center] (* Alonso del Arte, Jul 09 2009 *)


CROSSREFS

Row 1 = A067998(n) for n>0. Row 2 = A028387(n) for n>0.Column 1 = A000012(n). Column 2 = A001477. Column 3 = A005408(k). Column 4 = A016789(k+1). Column 5 = A004767(k+2). Column 6 = A016897(k+3). Column 7 = A016969(k+4). Column 8 = A017053(k+5). Column 9 = A004771(k+6). Column 10 = A017257(k+7).
Cf. A000012, A001477, A004767, A004771, A005408, A016789, A016897, A016969, A017053, A028387, A067998, A126719.
Sequence in context: A280633 A084614 A050058 * A048226 A049919 A246432
Adjacent sequences: A144201 A144202 A144203 * A144205 A144206 A144207


KEYWORD

easy,sign,tabl


AUTHOR

Jonathan Vos Post, Sep 13 2008


EXTENSIONS

Duplicate of 6th antidiagonal removed by R. J. Mathar, Jul 10 2009
Keyword:tabl added by R. J. Mathar, Jul 23 2009
Edited by N. J. A. Sloane, Sep 14 2009. There was a comment that the defining formula was wrong, but it is perfectly correct.


STATUS

approved



