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 1-6 of 6 results.

A038498 Matrix inverse of partition triangle A008284.

Original entry on oeis.org

1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, 0, -1, -1, 1, -1, 1, 1, 0, -1, -1, 1, -1, 0, 2, 0, 0, -1, -1, 1, 0, -1, 0, 2, 0, 0, -1, -1, 1, 0, -2, 1, 1, 1, 0, 0, -1, -1, 1, 1, -2, -1, 1, 1, 1, 0, 0, -1, -1, 1, 1, -1, -2, 0, 2, 0, 1, 0, 0, -1, -1, 1
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

Since A008284 has only ones in its first column, the sum of terms for any row n > 1 is 0. - François Marques, Feb 09 2021

Examples

			Triangle begins:
  1;
  -1,1;
  0,-1,1;
  1,-1,-1,1;
  ...

Crossrefs

Cf. A008284, A038497, A039800-A039810, A010815.

Programs

  • PARI
    tp(n, k) = if (n<1, 0, if (k<1, 0, if (k == n, 1, if (k > n, 0, tp(n-1, k-1) + tp(n-k, k)))));
tabl(nn) = {mtp = matrix(nn, nn, n, k, tp(n, k)); mtpi = mtp^(-1); for (n = 1, nn, for (k = 1, n, print1(mtpi[n, k], ", ");); print(););} \\ Michel Marcus, Mar 04 2014

Formula

T(n,n-k) = A010815(k) for k <= n/2. - François Marques, Feb 09 2021

A038497 Matrix square of partition triangle A008284.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 5, 5, 2, 1, 7, 8, 5, 2, 1, 11, 15, 10, 5, 2, 1, 15, 23, 18, 10, 5, 2, 1, 22, 38, 31, 20, 10, 5, 2, 1, 30, 56, 52, 34, 20, 10, 5, 2, 1, 42, 86, 83, 60, 36, 20, 10, 5, 2, 1, 56, 123, 129, 97, 63, 36, 20, 10, 5, 2, 1, 77, 181, 198, 158, 105, 65, 36, 20, 10, 5, 2, 1
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

Row sums form A022811 (number of terms in n-th derivative of a function composed with itself 3 times). - Paul D. Hanna, Jul 13 2004

Examples

			1; 2,1; 3,2,1; 5,5,2,1; ...

Crossrefs

Cf. A038498, A039800-A039809. a(n, 1) = A000041(n) (first column) (partition numbers).
Cf. A022811.

A039804 Column 5 of Inverse partition triangle A038498.

Original entry on oeis.org

1, -1, -1, 0, 0, 1, 1, 2, 0, 0, -1, -1, -2, -2, -2, -4, -1, -2, 0, 0, 3, 4, 6, 6, 8, 8, 10, 10, 9, 9, 7, 5, 2, 0, -7, -10, -18, -22, -29, -32, -41, -43, -49, -50, -54, -53, -54, -50, -46, -38, -30, -18, -6, 8, 25, 43, 62, 82, 108, 128, 155
Offset: 5

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Crossrefs

Cf. A039800-A039803.

Extensions

a(64) corrected by Sean A. Irvine, Feb 27 2021

A039803 Column 4 of inverse partition triangle A038498.

Original entry on oeis.org

1, -1, -1, 0, 0, 2, 1, 1, 0, -1, -1, -2, -3, -3, -2, -2, 0, 1, 3, 4, 6, 7, 9, 8, 10, 9, 8, 6, 3, -2, -5, -10, -16, -20, -27, -32, -37, -40, -44, -43, -47, -42, -42, -34, -30, -18, -12, 7, 17, 39, 53, 76, 92, 118, 133, 158, 175, 196, 210, 226, 237, 244
Offset: 4

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Links

Crossrefs

Cf. A038498, A039800, A039801, A039802, A039804.

Programs

  • PARI
    first(n) = { my(m = matrix(n + 4, n + 4)); for(i = 2, n + 4, m[i, i] = 1; ); for(k = 2, n + 4, for(i = k + 1, n + 4, m[i, k] = m[i - (k-1), k] + m[i-1,k-1] ) ); m = matrix(n + 3, n + 3, i, j, m[i + 1, j + 1])^-1; vector(n, i, m[i + 3, 4]) } \\ David A. Corneth, Feb 27 2021

Extensions

a(63) onward corrected by Sean A. Irvine, Feb 27 2021

A039801 Column 2 of Inverse partition triangle A038498.

Original entry on oeis.org

1, -1, -1, 1, 1, 1, 0, -1, -2, -2, -1, -1, 0, 2, 4, 4, 5, 5, 5, 2, 1, -2, -5, -8, -11, -14, -17, -18, -20, -18, -18, -11, -9, -1, 4, 15, 22, 34, 41, 54, 61, 70, 77, 83, 87, 87, 86, 80, 76, 59, 50, 27, 11, -19, -39, -78, -100, -143, -170, -216, -243, -290, -316
Offset: 2

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Crossrefs

Cf. A039800-A039804.

Extensions

a(61) onward corrected by Sean A. Irvine, Feb 27 2021

A039802 Column 3 of Inverse partition triangle A038498.

Original entry on oeis.org

1, -1, -1, 0, 1, 2, 0, 1, -1, -2, -2, -3, -2, -2, 1, 1, 3, 4, 7, 7, 8, 8, 7, 5, 2, -1, -6, -8, -15, -18, -24, -27, -31, -31, -35, -33, -30, -27, -21, -13, -4, 7, 21, 34, 51, 66, 84, 98, 117, 131, 145, 154, 164, 169, 170, 171, 164, 154, 141, 124, 94, 72, 34
Offset: 3

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Crossrefs

Cf. A039800-A039804.

Extensions

a(62) onward corrected by Sean A. Irvine, Feb 27 2021
Showing 1-6 of 6 results.

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

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