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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A125233 Triangle T(n,k) read by rows, the (n-k)-th term of the k times repeated partial sum of the hexagonal numbers, 0 <= k < n, 0 < n. 4
 1, 6, 1, 15, 7, 1, 28, 22, 8, 1, 45, 50, 30, 9, 1, 66, 95, 80, 39, 10, 1, 91, 161, 175, 119, 49, 11, 1, 120, 252, 336, 294, 168, 60, 12, 1, 153, 372, 588, 630, 462, 228, 72, 13, 1, 190, 525, 960, 1218, 1092, 690, 300, 85, 14, 1, 231, 715, 1485, 2178, 2310, 1782, 990, 385 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Left border = A000384, hexagonal numbers. The following columns are A002412, A002417, A034263, A051947, ... Row sums = (1, 7, 23, 59, 135, 291, ...) = A126284. A125232 is the analogous triangle for the pentagonal numbers. REFERENCES Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1964, p. 189. LINKS Table of n, a(n) for n=0..62. FORMULA T(n,0)=A000384(n). T(n,k) = T(n-1,k) + T(n-1,k-1), k>1. - R. J. Mathar, May 03 2008 EXAMPLE First few rows of the triangle: 1; 6, 1; 15, 7, 1; 28, 22, 8, 1; 45, 50, 30, 9, 1; 66, 95, 80, 39, 10, 1; 91, 161, 175, 119, 49, 11, 1; ... Example: (5,3) = 80 = 30 + 50 = (4,3) + (4,2). MAPLE A000384Psum:= proc(n, k) coeftayl( x*(1+3*x)/(1-x)^(3+k), x=0, n) ; end: A125233 := proc(n, k) A000384Psum(n-k, k) ; end: for n from 1 to 15 do for k from 0 to n -1 do printf("%d, ", A125233(n, k)) ; od: od: # R. J. Mathar, May 03 2008 CROSSREFS Cf. A000384, A002412, A002417, A034263, A051947, A125232. Sequence in context: A050309 A103217 A136273 * A139727 A257468 A278867 Adjacent sequences: A125230 A125231 A125232 * A125234 A125235 A125236 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Nov 24 2006 EXTENSIONS Edited and extended by R. J. Mathar, May 03 2008, and M. F. Hasler, Sep 29 2012 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.

Last modified May 28 15:01 EDT 2023. Contains 363019 sequences. (Running on oeis4.)