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.

A371999 Sums of antidiagonals of A372001.

Original entry on oeis.org

1, 2, 4, 10, 36, 219, 2778, 87238, 7310200, 1729159267, 1189189497342, 2549864969632543, 17220185517831384922, 394769893681270492415501, 30978809768092841795236288310, 8707079257583213762665388798383646, 9231279352362932208302062064694669246688
Offset: 0

Views

Author

Peter Luschny, Apr 21 2024

Keywords

Crossrefs

Cf. A372001.

A371994 Triangle read by rows: Related to the Euler numbers.

Original entry on oeis.org

1, 0, 1, 0, 1, 5, 0, 1, 19, 61, 0, 1, 42, 498, 1385, 0, 1, 74, 1932, 19238, 50521, 0, 1, 115, 5290, 114830, 1057475, 2702765, 0, 1, 165, 11805, 449539, 8949633, 79160457, 199360981, 0, 1, 224, 23016, 1360198, 47306246, 899141244, 7768928932, 19391512145
Offset: 0

Views

Author

Peter Luschny, Apr 21 2024

Keywords

Comments

Inspired by Philippe Deléham's formula for A371637.

Examples

			Triangle starts:
  [0] [1]
  [1] [0, 1]
  [2] [0, 1,   5]
  [3] [0, 1,  19,    61]
  [4] [0, 1,  42,   498,   1385]
  [5] [0, 1,  74,  1932,  19238,   50521]
  [6] [0, 1, 115,  5290, 114830, 1057475,  2702765]
  [7] [0, 1, 165, 11805, 449539, 8949633, 79160457, 199360981]
		

Crossrefs

Cf. A000364 (main diagonal), A371637, A371765 (row sums), A372001.
Cf. A084938.

Programs

  • SageMath
    # Using function GeneralizedDelehamDelta from A372001.
    def A371994_triangle(dim):
        a = lambda n: n % 2
        b = lambda n: (n + 1)^2
        return GeneralizedDelehamDelta([a, b], dim, False)
    for row in A371994_triangle(8): print(row)

Formula

Triangle T given by [0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined by Deléham in A084938.
Showing 1-2 of 2 results.