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.

Previous Showing 31-33 of 33 results.

A159756 Triangle A159755 reversed .

Original entry on oeis.org

0, 1, -1, 4, -1, -2, 12, 0, -3, -3, 32, 4, -4, -5, -4, 80, 16, -4, -8, -7, -5, 192, 48, 0, -12, -12, -9, -6, 448, 128, 16, -16, -20, -16, -11, -7, 1024, 320, 64, -16, -32, -28, -20, -13, -8, 2304, 768, 192, 0, -48, -48, -36, -24, -15, -9
Offset: 0

Views

Author

Philippe Deléham, Apr 21 2009

Keywords

Examples

			Triangle begins : 0 ; 1,-1 ; 4,-1,-2 ; 12,0,-3,-3 ; 32,4,-4,-5,-4 ; ...

Crossrefs

Cf. A062111, A152920

Formula

Sum_{k=0..n} T(n,k) = A045618(n-2) for n>=2 . T(2n,n)=-A001787(n).

A317450 a(n)=(-1)^((n-2)*(n-1)/2)*2^((n-1)^2)*n^(n-3).

Original entry on oeis.org

1, 1, -16, -2048, 1638400, 7247757312, -164995463643136, -18446744073709551616, 9803356117276277820358656, 24178516392292583494123520000000, -271732164163901599116133024293512544256, -13717048991958695477963985711266803110069141504, 3074347100178259797134292590832254504315406543889629184
Offset: 1

Views

Author

Rigoberto Florez, Aug 26 2018

Keywords

Comments

Discriminant of Pell polynomials.
Pell polynomials are defined as P(0)=0, P(1)=1 and P(n)=2xP(n-1)+P(n-2) for n>1.

Links

Crossrefs

Cf. A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A193678, A317404, A317405, A317408, A317451, A318184, A318197.
Essentially the same as A086804.

Programs

  • Mathematica
    Array[(-1)^((#-2)*(#-1)/2)* 2^((#-1)^2)*#^(#-3)&,15]

A337631 a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,...,n}.

Original entry on oeis.org

0, 1, 10, 55, 228, 801, 2526, 7387, 20440, 54229, 139218, 348111, 851916, 2047945, 4849606, 11337667, 26214336, 60030909, 136314810, 307232695, 687865780, 1530920881, 3388997550, 7465861035, 16374562728, 35769024421, 77846282146, 168845901727
Offset: 1

Views

Author

Enrique Navarrete, Sep 20 2020

Keywords

Comments

Partial sums of A036826.
For the sum of diameters of subsets of {1,2,...,n} see A045618.

Examples

			For n = 3, the nonempty subsets of {1,2,3} are {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}; the diameters of these sets are 0,0,0,1,1,2,2 and the sum of the squares of these numbers is 10.

Links

Crossrefs

Cf. A036826, A045618.

Formula

From Stefano Spezia, Sep 21 2020: (Start)
G.f.: x*(1 + 2*x)/((1 - x)^2*(1 - 2*x)^3).
a(n) = 8*a(n-1) - 25*a(n-2) + 38*a(n-3) - 28*a(n-4) + 8*a(n-5) for n > 4.
a(n) = 2^(n+1)*(n^2 - 4*n + 8) - 3*n - 16. (End)
Previous Showing 31-33 of 33 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.