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 1-3 of 3 results.

A128090 Denominators in inverse of A128077, numerators = 1.

Original entry on oeis.org

1, -4, 4, -18, -18, 9, -48, -48, -48, 16, -100, -100, -100, -100, 25, -180, -180, -180, -180, -180, 36, -294, -294, -294, -294, -294, -294, 49
Offset: 1

Views

Author

Gary W. Adamson, Feb 14 2007

Keywords

Comments

Row sums of the inverse of A128077: (1/1; -1/4, 1/4; -1/18, -1/18, 1/9; ...) = (1, 0, 0, 0, ...).
Row sums of unsigned terms: (1; 4, 4; 18, 18, 9; ...) = A128091.
A045991 = (0, 0, 4, 18, 48, 100, ...).

Examples

			First few rows of the triangle:
     1
    -4,    4;
   -18,  -18,    9;
   -48,  -48,  -48,   16;
  -100, -100, -100, -100, 25;
  ...

Crossrefs

Cf. A128077, A045991, A128091.

Formula

Denominators in inverse triangular matrix of A128077, i.e., inverse of (1; 1, 4; 1, 2, 9; 1, 2, 3, 16; ...).

A128078 A002260 * A128064.

Original entry on oeis.org

1, -1, 4, -1, -2, 9, -1, -2, -3, 16, -1, -2, -3, -4, 25, -1, -2, -3, -4, -5, 36, -1, -2, -3, -4, -5, -6, 49, -1, -2, -3, -4, -5, -6, -7, 64
Offset: 1

Views

Author

Gary W. Adamson, Feb 14 2007

Keywords

Comments

Row sums = the triangular numbers: (1, 3, 6, 10, ...).
Row sums of A128077 = A000326, the pentagonal numbers: (1, 5, 12, 22, 35, ...).

Examples

			First few rows of the triangle:
   1;
  -1,  4;
  -1, -2,  9;
  -1, -2, -3, 16;
  ...

Crossrefs

Cf. A002260, A128064, A128077, A000326.

Formula

A002260 * A128064 as infinite lower triangular matrices. Retain the right border of A128077 and change the signs of all other terms to (-).

A128091 Row sums of unsigned A128090.

Original entry on oeis.org

1, 8, 45, 160, 425, 936, 1813, 3200, 5265, 8200, 12221, 17568, 24505, 33320, 44325, 57856, 74273, 93960, 117325, 144800, 176841, 213928, 256565, 305280, 360625, 423176, 493533, 572320, 660185, 757800, 865861, 985088, 1116225, 1260040, 1417325
Offset: 1

Views

Author

Gary W. Adamson, Feb 14 2007

Keywords

Examples

			a(4) = 160 = sum of row 4 terms of A128090: (48 + 48 + 48 + 16) = 3*A045991(4) + 4^2; where A045991 = (0, 0, 4, 18, 48, 100, ...).

Links

Crossrefs

Cf. A000290, A002522, A128077, A128090, A045991.

Programs

Formula

a(n) = (n-1)*A045991(n) + n^2.
a(n) = n^2*(n^2 - 2*n + 2) = A000290(n)*A002522(n-1). - Philippe Deléham, Mar 16 2014
G.f.: x*(1 + 3*x + 15*x^2 + 5*x^3)/(1-x)^5. - Philippe Deléham, Mar 16 2014
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), a(1) = 1, a(2) = 8, a(3) = 45, a(4) = 160, a(5) = 425. - Philippe Deléham, Mar 16 2014

Extensions

a(10)-a(35) from Philippe Deléham, Mar 16 2014
Showing 1-3 of 3 results.

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

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