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!)
A176282 Triangle T(n,k) = 1 + A000330(n) - A000330(k) - A000330(n-k), read by rows. 2
1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 21, 16, 1, 1, 25, 37, 37, 25, 1, 1, 36, 57, 64, 57, 36, 1, 1, 49, 81, 97, 97, 81, 49, 1, 1, 64, 109, 136, 145, 136, 109, 64, 1, 1, 81, 141, 181, 201, 201, 181, 141, 81, 1, 1, 100, 177, 232, 265, 276, 265, 232, 177, 100, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Not summing squares but summing integers implied by the definition (i.e., not using A000330 but A000217) gives A077028.

Row sums = {1, 2, 6, 20, 55, 126, 252, 456, 765, 1210, 1826, ...} = (n+1)*(n+2)*(n^2-2*n+3)/6.

LINKS

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

FORMULA

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

T(n,k) = 1 + k*(n+1)*(n-k). - G. C. Greubel, Nov 24 2019

EXAMPLE

Triangle begins as:

  1;

  1,   1;

  1,   4,   1;

  1,   9,   9,   1;

  1,  16,  21,  16,   1;

  1,  25,  37,  37,  25,   1;

  1,  36,  57,  64,  57,  36,   1;

  1,  49,  81,  97,  97,  81,  49,   1;

  1,  64, 109, 136, 145, 136, 109,  64,   1;

  1,  81, 141, 181, 201, 201, 181, 141,  81,   1;

  1, 100, 177, 232, 265, 276, 265, 232, 177, 100, 1;

MAPLE

seq(seq(1 + k*(n+1)*(n-k), k=0..n), n=0..12); # G. C. Greubel, Nov 24 2019

MATHEMATICA

(* Sequence for q=1..10 *)

f[n_, k_, q_]:= f[n, k, q] = 1 +Sum[i^q, {i, 0, n}] -Sum[i^q, {i, 0, k}] + Sum[i^q, {i, 0, n-k}]; Table[Flatten[Table[f[n, k, q], {n, 0, 12}, {k, 0, n}]], {q, 1, 10}]

(* Second program *)

Table[1 + k*(n+1)*(n-k), {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 24 2019 *)

PROG

(PARI) T(n, k) = 1 + k*(n+1)*(n-k); \\ G. C. Greubel, Nov 24 2019

(MAGMA) [1 + k*(n+1)*(n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 24 2019

(Sage) [[1 + k*(n+1)*(n-k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 24 2019

(GAP) Flat(List([0..12], n-> List([0..n], k-> 1 + k*(n+1)*(n-k) ))); # G. C. Greubel, Nov 24 2019

CROSSREFS

Cf. A077028.

Sequence in context: A308359 A199065 A152237 * A082043 A177944 A174006

Adjacent sequences:  A176279 A176280 A176281 * A176283 A176284 A176285

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 May 25 08:26 EDT 2020. Contains 334585 sequences. (Running on oeis4.)