login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A081422 Triangle read by rows in which row n consists of the first n+1 n-gonal numbers. 9
1, 1, 1, 1, 2, 3, 1, 3, 6, 10, 1, 4, 9, 16, 25, 1, 5, 12, 22, 35, 51, 1, 6, 15, 28, 45, 66, 91, 1, 7, 18, 34, 55, 81, 112, 148, 1, 8, 21, 40, 65, 96, 133, 176, 225, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

T. D. Noe, Rows n = 0..100 of triangle, flattened

Eric Weisstein's World of Mathematics, Polygonal Number

FORMULA

Array of coefficients of x in the expansions of T(k, x) = (1 + k*x -(k-2)*x^2)/(1-x)^4, k > -4.

T(n, k) = k*((n-2)*k -(n-4))/2 (see MathWorld link). - Michel Marcus, Jun 22 2015

EXAMPLE

The array starts

  1  1  3 10 ...

  1  2  6 16 ...

  1  3  9 22 ...

  1  4 12 28 ...

The triangle starts

  1;

  1,  1;

  1,  2,  3;

  1,  3,  6, 10;

  1,  4,  9, 16, 25;

  ...

MATHEMATICA

Table[PolygonalNumber[n, i], {n, 0, 10}, {i, n+1}]//Flatten (* Requires Mathematica version 10.4 or later *) (* Harvey P. Dale, Aug 27 2016 *)

PROG

(PARI) tabl(nn) = {for (n=0, nn, for (k=1, n+1, print1(k*((n-2)*k-(n-4))/2, ", "); ); print(); ); } \\ Michel Marcus, Jun 22 2015

(MAGMA) [[k*((n-2)*k-(n-4))/2: k in [1..n+1]]: n in [0..10]]; // G. C. Greubel, Oct 13 2018

(Sage) [[k*((n-2)*k -(n-4))/2 for k in (1..n+1)] for n in (0..10)] # G. C. Greubel, Aug 14 2019

(GAP) Flat(List([0..10], n-> List([1..n+1], k-> k*((n-2)*k-(n-4))/2 ))); # G. C. Greubel, Aug 14 2019

CROSSREFS

Rows include A060354, A064808, A000600, A000603, A002411.

Diagonals include A001093, A053698, A069778, A000578, A002414, A081423, A081435, A081436, A081437, A081438, A081441.

Antidiagonals are composed of n-gonal numbers.

Sequence in context: A208516 A111808 A247046 * A213742 A213743 A213744

Adjacent sequences:  A081419 A081420 A081421 * A081423 A081424 A081425

KEYWORD

easy,nonn,tabl,look

AUTHOR

Paul Barry, Mar 21 2003

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)