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 1-4 of 4 results.

A173796 Partial sums of A051489.

Original entry on oeis.org

1, 5, 37, 405, 5797, 100729, 2042489, 47179065, 1220920889, 34959928189, 1096877292413, 37411749830381, 1378024126754541, 54510112209204673, 2304521044056503745, 103693069431259678913, 4947499083397499144385
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 24 2010

Keywords

Links

Crossrefs

Cf. A051489.

Programs

  • Magma
    [(&+[j^(j+2) + (j+2)^j: j in [0..n]]): n in [0..40]]; // G. C. Greubel, Jul 14 2021
  • Mathematica
    f[n_]:=(n^(n+2)+(n+2)^n); s=0; Table[s+=f[n],{n,0,40}]
  • Sage
    [sum(j^(j+2) + (j+2)^j for j in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 14 2021

Formula

a(n) = Sum_{j=0..n} A051489(j). - G. C. Greubel, Jul 14 2021

A055652 Table T(m,k)=m^k+k^m (with 0^0 taken to be 1) as square array read by antidiagonals.

Original entry on oeis.org

2, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 5, 17, 17, 5, 1, 1, 6, 32, 54, 32, 6, 1, 1, 7, 57, 145, 145, 57, 7, 1, 1, 8, 100, 368, 512, 368, 100, 8, 1, 1, 9, 177, 945, 1649, 1649, 945, 177, 9, 1, 1, 10, 320, 2530, 5392, 6250, 5392, 2530, 320, 10, 1, 1, 11, 593, 7073
Offset: 0

Views

Author

Henry Bottomley, Jun 08 2000

Keywords

Crossrefs

Columns and rows are A000012 (apart from first term), A000027, A001580, A001585, A001589, A001593 etc. Diagonals include A013499 (apart from first two terms), A051442, A051489.
Cf. A055651.
Contribution from Franklin T. Adams-Watters, Oct 26 2009: (Start)
Rows/columns: A000027, A001580, A001585, A001589, A001593, A001594, A001596.
Main diagonal is 2 * A000312. More diagonals: A051442, A051489, A155539.
Cf. A076980, A156353, A156354. (End)

Formula

E.g.f. Sum(n,m, T(n,m)/(n! m!)) = e^(x e^y) + e^(y e^x). [From Franklin T. Adams-Watters, Oct 26 2009]

A155539 a(n) = n^(n+3) + (n+3)^n.

Original entry on oeis.org

1, 5, 57, 945, 18785, 423393, 10609137, 292475249, 8804293473, 287589316833, 10137858491849, 383799398752905, 15536767912476993, 669920208810550337, 30659724555890596833, 1484638520651877849057, 75846305139481944586817
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 23 2009

Keywords

Comments

1^4 + 4^1 = 5, 2^5 + 5^2 = 57, ...

Links

Crossrefs

Cf. A046065, A051442, A007925, A051489, A153217, A076980.

Programs

  • Magma
    [n^(n+3)+(n+3)^n: n in [0..20] ]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    lst={};Do[m=n+3;q=n^m+m^n;AppendTo[lst,q],{n,0,4!}];lst
Table[n^(n+3)+(n+3)^n,{n,0,20}] (* Harvey P. Dale, Aug 18 2024 *)

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 24 2011

A154569 Partial sums of (2n-1)^(2n+1)+(2n+1)^(2n-1).

Original entry on oeis.org

0, 4, 372, 95304, 45231880, 33784239180, 36348656777148, 53168436739227280, 101441716823942402448, 244654264259760069435540, 727702646597963991868772740, 2616780161875511741808194232024, 11190492899233441015089845457437592
Offset: 0

Views

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 12 2009

Keywords

Comments

All the terms of the sequence are divisible by 4, a(0) = 0 by default.

Crossrefs

Cf. A154682.

Programs

  • Mathematica
    Accumulate[Table[(2n-1)^(2n+1)+(2n+1)^(2n-1),{n,20}]] (* Harvey P. Dale, Jun 05 2012 *)

Formula

a(n) = a(n-1)+(2n-1)^(2n+1)+(2n+1)^(2n-1).
a(n) = sum_{k=0..n} A051489(2k-1). - R. J. Mathar, Jan 14 2009

Extensions

More terms from Harvey P. Dale, Jun 05 2012
Showing 1-4 of 4 results.

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