login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125232 Triangle T(n,k) read by rows: the (n-k)-th term of the k-fold iterated partial sum of the pentagonal numbers. 7
1, 5, 1, 12, 6, 1, 22, 18, 7, 1, 35, 40, 25, 8, 1, 51, 75, 65, 33, 9, 1, 70, 126, 140, 98, 42, 10, 1, 92, 196, 266, 238, 140, 52, 11, 1, 117, 288, 462, 504, 378, 192, 63, 12, 1, 145, 405, 750, 966, 882, 570, 255, 75, 13, 1, 176, 550, 1155, 1716, 1848, 1452, 825, 330, 88, 14, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966, p 189.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10011(rows 0 to 140, flattened)
FORMULA
T(n,0)=A000326(n). T(n,k)=T(n-1,k) + T(n-1,k-1), k>0. - R. J. Mathar, Jun 09 2008
G.f. as triangle: (1+2*x)/((1-x)^2*(1-x-x*y)). - Robert Israel, Nov 07 2016
EXAMPLE
First few rows of the triangle are:
1;
5, 1;
12, 6, 1;
22, 18, 7, 1;
35, 40, 25, 8, 1;
51, 75, 65, 33, 9, 1;
70, 126, 140, 98, 42, 10, 1;
...
Example: (5,3) = 65 = 25 + 40 = (4,3) + (4,2).
MAPLE
A125232 := proc(n, k) option remember ; if k = 0 then A000326(n) ; elif k = n-1 then 1 ; else procname(n-1, k)+procname(n-1, k-1) ; fi : end: # R. J. Mathar, Jun 09 2008
MATHEMATICA
nmax = 11; col[1] = Table[n(3n-1)/2, {n, 1, nmax}]; col[k_] := col[k] = Prepend[Accumulate[col[k-1]], 0]; Table[col[k][[n]], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 25 2019 *)
CROSSREFS
Columns: A000326 (pentagonal numbers), A002411, A001296, A051836, A051923.
Cf. A095264 (row sums).
Sequence in context: A146993 A343223 A104572 * A116923 A327797 A062264
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 24 2006
EXTENSIONS
Edited and extended by R. J. Mathar, Jun 09 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)