cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A125199 Triangle read by rows: T(n,k) = 4*n*k - n - k, 1<=k<=n.

Original entry on oeis.org

2, 5, 12, 8, 19, 30, 11, 26, 41, 56, 14, 33, 52, 71, 90, 17, 40, 63, 86, 109, 132, 20, 47, 74, 101, 128, 155, 182, 23, 54, 85, 116, 147, 178, 209, 240, 26, 61, 96, 131, 166, 201, 236, 271, 306, 29, 68, 107, 146, 185, 224, 263, 302, 341, 380, 32, 75, 118, 161, 204, 247
Offset: 1

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Author

Reinhard Zumkeller, Nov 24 2006

Keywords

Comments

A124934 gives the range: for n,k with 1<=k<=n exists at least one m such that A124934(m)=T(n,k);
row sums give A125200; central terms give A125201;
T(n,1) = A016789(n-1);
T(n,2) = A017041(n-1) for n>1;
T(n,3) = A017485(n-1) for n>2;
T(n,n-1) = A125202(n) for n>1;
T(n,n) = A002939(n).

Programs

  • Mathematica
    Flatten[Table[4*n*k-n-k,{n,15},{k,n}]] (* Harvey P. Dale, Nov 15 2014 *)

A360417 a(n) = 8*n^2 - 7*n + 2.

Original entry on oeis.org

2, 3, 20, 53, 102, 167, 248, 345, 458, 587, 732, 893, 1070, 1263, 1472, 1697, 1938, 2195, 2468, 2757, 3062, 3383, 3720, 4073, 4442, 4827, 5228, 5645, 6078, 6527, 6992, 7473, 7970, 8483, 9012, 9557, 10118, 10695, 11288, 11897, 12522, 13163, 13820, 14493, 15182
Offset: 0

Views

Author

James Propp, Feb 06 2023

Keywords

Comments

This is one of the four quadratic sequences that, interleaved, yield A360418.

Links

Crossrefs

Cf. A051870, A125201, A360416, A360418.

Programs

  • Mathematica
    Table[8*n^2 - 7*n + 2, {n, 0, 100}]

Formula

From Elmo R. Oliveira, Jan 28 2025: (Start)
G.f.: (17*x^2-3*x+2)/(1-x)^3.
E.g.f.: exp(x)*(2 + x + 8*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3.
a(n) = A360418(4*n-1) for n>=1. (End)
a(n) = A125201(n) + 1, n >= 1. - Omar E. Pol, Jan 28 2025

Extensions

a(0)=2 prepended and more terms from Alois P. Heinz, Jan 28 2025
Showing 1-2 of 2 results.

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