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.

A368046 a(n) = ((n + 1)^2 * (5*n + 4)*n) / 12.

Original entry on oeis.org

0, 3, 21, 76, 200, 435, 833, 1456, 2376, 3675, 5445, 7788, 10816, 14651, 19425, 25280, 32368, 40851, 50901, 62700, 76440, 92323, 110561, 131376, 155000, 181675, 211653, 245196, 282576, 324075, 369985, 420608, 476256, 537251
Offset: 0

Views

Author

Peter Luschny, Dec 09 2023

Keywords

Links

Crossrefs

Cf. A368045.

Programs

  • Mathematica
    A368046[n_]:=((n+1)^2(5n+4)n)/12;Array[A368046,50,0] (* or *)
LinearRecurrence[{5,-10,10,-5,1},{0,3,21,76,200},50] (* Paolo Xausa, Dec 10 2023 *)

Formula

a(n) = Sum_{k=0..n} A368045(k).
G.f.: x*(3 + 6*x + x^2)/(1 - x)^5. - Stefano Spezia, Dec 10 2023

A368047 a(n) = (-1)^n * n*(n + 1)*(2*n + (-1)^n * (4*n + 5) + 1) / 12.

Original entry on oeis.org

0, 1, 9, 10, 50, 35, 147, 84, 324, 165, 605, 286, 1014, 455, 1575, 680, 2312, 969, 3249, 1330, 4410, 1771, 5819, 2300, 7500, 2925, 9477, 3654, 11774, 4495, 14415, 5456, 17424, 6545, 20825, 7770, 24642, 9139, 28899, 10660, 33620, 12341
Offset: 0

Views

Author

Peter Luschny, Dec 09 2023

Keywords

Links

Crossrefs

Cf. A368045, A368046.

Programs

  • Mathematica
    A368047[n_]:=n(n+1)(2n+(-1)^n(4n+5)+1)(-1)^n/12;Array[A368047,50,0] (* or *)
LinearRecurrence[{0,4,0,-6,0,4,0,-1},{0,1,9,10,50,35,147,84},50] (* Paolo Xausa, Dec 10 2023 *)

Formula

a(n) = Sum_{n=0..k} (-1)^(n-k) *A368045(n, k).
G.f.: x*(1 + 9*x + 6*x^2 + 14*x^3 + x^4 + x^5)/((1 - x)^4*(1 + x)^4). - Stefano Spezia, Dec 10 2023
Showing 1-2 of 2 results.

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