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.

A262067 a(n) = n^n - (n-2)^n.

Original entry on oeis.org

2, 4, 26, 240, 2882, 42560, 745418, 15097600, 347066882, 8926258176, 253930611002, 7916100448256, 268352394448322, 9828088361009152, 386707997366768618, 16268790735900180480, 728714136550643404802, 34624041592426892361728
Offset: 1

Views

Author

Altug Alkan, Sep 10 2015

Keywords

Comments

Inspired by multi-dimensional cubes: For n>1, the number of lattice points on the surface of a k-dimensional cube with side-length n is f(n,k) = n^k - (n-2)^k. a(n) = f(n,n).

Examples

			For n = 2, a(n) = n^n - (n-2)^n = 2^2 - (2-2)^2 = 4.

Crossrefs

Cf. A000312, A008788.
For sequences with "Number of points on surface of k-dimensional cube," cf. A130130 (k=1), A008574 (k=2, shifted), A005897 (k=3), A008511 (k=4), A008512 (k=5), A008513 (k=6).

Programs

Formula

a(n) = A000312(n) - A008788(n-2).

A385897 a(n) = 1 - 5*(n + 1)^2 + 5*(n + 1)^4.

Original entry on oeis.org

1, 61, 361, 1201, 3001, 6301, 11761, 20161, 32401, 49501, 72601, 102961, 141961, 191101, 252001, 326401, 416161, 523261, 649801, 798001, 970201, 1168861, 1396561, 1656001, 1950001, 2281501, 2653561, 3069361, 3532201, 4045501, 4612801, 5237761, 5924161, 6675901
Offset: 0

Views

Author

Peter Luschny, Jul 21 2025

Keywords

Links

Crossrefs

Cf. A385896 (column 5), A063497, A000290, A061317, A022521, A008512.

Programs

  • Maple
    gf := (-x^4 + 4*x^3 - 66*x^2 - 56*x - 1)/(x - 1)^5:
ser := series(gf, x, 35): seq(coeff(ser, x, n), n = 0..33);
  • Mathematica
    a[n_] := With[{h = (n + 1)^2}, 5 (h^2 - h) + 1]; Table[a[n], {n, 0, 33}]

Formula

a(n) = [x^n] (-x^4 + 4*x^3 - 66*x^2 - 56*x - 1)/(x - 1)^5.
a(n) = 5! * [x^5] (1 - sin(n*x))^(-1/n) for n > 0.
a(n) = A385896(n + 5, 5).
A000290(n) = (a(n) - 2*a(n-1) + a(n-2)) / 60.
A008512(n) = (a(n) + 2*a(n-1) + a(n-2)) / 2.
A022521(n) = (a(n-1) + a(n)) / 2.
A061317(n) = (a(n) - a(n-2)) / 20.
A063497(n) = a(n) - a(n-1).
gcd(a(n), a(n+1)) = 1.
Showing 1-2 of 2 results.

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