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A101321 Table T(n,m) = 1 + n*m*(m+1)/2 read by antidiagonals: centered polygonal numbers. 26
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 7, 7, 4, 1, 1, 11, 13, 10, 5, 1, 1, 16, 21, 19, 13, 6, 1, 1, 22, 31, 31, 25, 16, 7, 1, 1, 29, 43, 46, 41, 31, 19, 8, 1, 1, 37, 57, 64, 61, 51, 37, 22, 9, 1, 1, 46, 73, 85, 85, 76, 61, 43, 25, 10, 1, 1, 56, 91, 109, 113, 106, 91, 71, 49, 28, 11, 1, 1, 67 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row n gives the centered figurate numbers of the n-gon.
Antidiagonal sums are in A101338.
LINKS
FORMULA
T(n,2) = A016777(n). T(n,3) = A016921(n). T(n,4) = A017281(n).
T(10,m) = A062786(m+1).
T(11,m) = A069125(m+1).
T(12,m) = A003154(m+1).
T(13,m) = A069126(m+1).
T(14,m) = A069127(m+1).
T(15,m) = A069128(m+1).
T(16,m) = A069129(m+1).
T(17,m) = A069130(m+1).
T(18,m) = A069131(m+1).
T(19,m) = A069132(m+1).
T(20,m) = A069133(m+1).
T(n+1,m) = T(n,m) + m*(m+1)/2. - Gary W. Adamson and Michel Marcus, Oct 13 2015
EXAMPLE
The upper left corner of the infinite array T is
|0| 1 1 1 1 1 1 1 1 1 1 ... A000012
|1| 1 2 4 7 11 16 22 29 37 46 ... A000124
|2| 1 3 7 13 21 31 43 57 73 91 ... A002061
|3| 1 4 10 19 31 46 64 85 109 136 ... A005448
|4| 1 5 13 25 41 61 85 113 145 181 ... A001844
|5| 1 6 16 31 51 76 106 141 181 226 ... A005891
|6| 1 7 19 37 61 91 127 169 217 271 ... A003215
|7| 1 8 22 43 71 106 148 197 253 316 ... A069099
|8| 1 9 25 49 81 121 169 225 289 361 ... A016754
|9| 1 10 28 55 91 136 190 253 325 406 ... A060544
MAPLE
A101321 := proc(n, k)
n*k*(k+1)/2+1 ;
end proc: # R. J. Mathar, Jul 28 2016
MATHEMATICA
T[n_, m_] := 1 + n m (m + 1)/2;
Table[T[n - m, m], {n, 0, 12}, {m, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 23 2020 *)
PROG
(Iverson's J language) Let cfn be the formula above. Then the first 20 rows and columns of T are: T =: cfn / ~ i. 20 where i.
(PARI) T(n, m) = 1 + n*m*(m+1)/2 \\ Charles R Greathouse IV, Jul 28 2016
CROSSREFS
Sequence in context: A058717 A034371 A318951 * A210764 A091186 A138155
KEYWORD
easy,nonn,tabl
AUTHOR
Eugene McDonnell (eemcd(AT)mac.com), Dec 24 2004
EXTENSIONS
Edited by R. J. Mathar, Oct 21 2009
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)