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!)
A176284 Triangle T(n,k) = 1 + 3*n*k*(n-k) read by rows. 2
1, 1, 1, 1, 7, 1, 1, 19, 19, 1, 1, 37, 49, 37, 1, 1, 61, 91, 91, 61, 1, 1, 91, 145, 163, 145, 91, 1, 1, 127, 211, 253, 253, 211, 127, 1, 1, 169, 289, 361, 385, 361, 289, 169, 1, 1, 217, 379, 487, 541, 541, 487, 379, 217, 1, 1, 271, 481, 631, 721, 751, 721, 631, 481, 271, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

This could be written T(n,k) = 1 - (n-k)^3 - k^3 + n^3, where squares (instead of cubes) would define A130154.

Row sums are {1, 2, 9, 40, 125, 306, 637, 1184, 2025, 3250, 4961, ...} = (n+1)^2*(n^2 -2*n +2)/2.

LINKS

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

FORMULA

T(n,k) = T(n,n-k).

T(n,k) = 1 + 3*n*k*(n-k).

EXAMPLE

Triangle begins as:

  1;

  1,   1;

  1,   7,   1;

  1,  19,  19,   1;

  1,  37,  49,  37,   1;

  1,  61,  91,  91,  61,   1;

  1,  91, 145, 163, 145,  91,   1;

  1, 127, 211, 253, 253, 211, 127,   1;

  1, 169, 289, 361, 385, 361, 289, 169,   1;

  1, 217, 379, 487, 541, 541, 487, 379, 217,   1;

  1, 271, 481, 631, 721, 751, 721, 631, 481, 271, 1;

MAPLE

seq(seq(1 + 3*n*k*(n-k), k=0..n), n=0..12); # G. C. Greubel, Nov 25 2019

MATHEMATICA

Flatten[Table[1+3n k(n-k), {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Jul 03 2013 *)

PROG

(PARI) T(n, k) = 1 + 3*n*k*(n-k); \\ G. C. Greubel, Nov 25 2019

(MAGMA) [1 + 3*n*k*(n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 25 2019

(Sage) [[1 + 3*n*k*(n-k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 25 2019

(GAP) Flat(List([0..12], n-> List([0..n], k-> 1 + 3*n*k*(n-k) ))); # G. C. Greubel, Nov 25 2019

CROSSREFS

Cf. A130154.

Sequence in context: A275526 A141597 A176561 * A154233 A174033 A119727

Adjacent sequences:  A176281 A176282 A176283 * A176285 A176286 A176287

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Apr 14 2010

EXTENSIONS

Edited by R. J. Mathar, May 03 2013

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 July 13 04:01 EDT 2020. Contains 335673 sequences. (Running on oeis4.)