A094415 - OEIS

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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A094415

Triangle T read by rows: dot product <r,r-1,...,1> * <s+1,s+2,...,r,1,2,...,s>.

1, 4, 5, 10, 13, 13, 20, 26, 28, 26, 35, 45, 50, 50, 45, 56, 71, 80, 83, 80, 71, 84, 105, 119, 126, 126, 119, 105, 120, 148, 168, 180, 184, 180, 168, 148, 165, 201, 228, 246, 255, 255, 246, 228, 201, 220, 265, 300, 325, 340, 345, 340, 325, 300, 265, 286, 341

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

T(n, k) = n*(n^2 + 3*n*(1+k) + 2 - 3*k^2)/6 for n >= 0, 0 <= k <= n.

EXAMPLE

Triangle begins as:

4, 5;

10, 13, 13;

20, 26, 28, 26;

35, 45, 50, 50, 45;

56, 71, 80, 83, 80, 71;

MAPLE

seq(seq( (n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6 , k=0..n), n=0..12); # G. C. Greubel, Oct 30 2019

MATHEMATICA

Table[(n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 30 2019 *)

PROG

(PARI) T(n, k) = (n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6;

for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Oct 30 2019

(Magma) [(n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6: k in [0..n], n in [0..12]]; // G. C. Greubel, Oct 30 2019

(Sage) [[(n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Oct 30 2019

(GAP) Flat(List([0..12], n-> List([0..n], k-> (n+1)*((n+2)*(n+3) + 3*k*(n-k+1))/6 ))); # G. C. Greubel, Oct 30 2019

CROSSREFS

Columns 0-6 are A000292, A008778, A026054, A026057, A026060, A026063, A026066.

Half-diagonal is A050410.

Row sums are A000537.

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.