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.

A275963 First differences of A265908; second differences of A265907.

Original entry on oeis.org

18, 234, 2244, 22098, 237594, 2743164, 33556818, 441925794, 12449045364, 267703255698, 5497712563434, 112804699752300, 2358022995718578, 51007863864388434, 1135446810698914644, 26241095309660220138, 626391138692542250154, 15519080113275337003404, 397364781519139001021778, 10545585096254938755221394, 289700229771377481566636364
Offset: 1

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Crossrefs

Row 3 of A275960.

Programs

Formula

a(n) = A265908(1+n) - A265908(n).

A275960 Square array A(1,k) = A265907(k), A(n>1,k) = A(n-1, k+1) - A(n-1, k); successive differences of A265907 read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Original entry on oeis.org

1, 5, 4, 27, 22, 18, 283, 256, 234, 216, 2783, 2500, 2244, 2010, 1794, 27381, 24598, 22098, 19854, 17844, 16050, 289573, 262192, 237594, 215496, 195642, 177798, 161748, 3294929, 3005356, 2743164, 2505570, 2290074, 2094432, 1916634, 1754886, 39857103, 36562174, 33556818, 30813654, 28308084, 26018010, 23923578, 22006944, 20252058
Offset: 1

Views

Author

Antti Karttunen, Aug 13 2016

Keywords

Examples

			The top left corner of the array:
       1, 5, 27, 283, 2783, 27381, 289573
       4, 22, 256, 2500, 24598, 262192, 3005356
      18, 234, 2244, 22098, 237594, 2743164, 33556818
     216, 2010, 19854, 215496, 2505570, 30813654, 408368976
    1794, 17844, 195642, 2290074, 28308084, 377555322, 11598750594
   16050, 177798, 2094432, 26018010, 349247238, 11221195272, 231648340170
  161748, 1916634, 23923578, 323229228, 10871948034, 220427144898, ...
		

Crossrefs

Transpose: A275961.
Row 1: A265907, row 2: A265908, row 3: A275963.
Column 1: A275965.
Cf. A255411.
Variant: A275950.

Programs

Formula

A(1,k) = A265907(k); and for n > 1, A(n,k) = A(n-1, k+1) - A(n-1, k).

A265907 a(1) = 1; for n > 1, a(n) = a(n-1) + A255411(a(n-1)).

Original entry on oeis.org

1, 5, 27, 283, 2783, 27381, 289573, 3294929, 39857103, 518345071, 13445878403, 294076667433, 6072420019897, 124655463124661, 2601261501948003, 56085731405159779, 1245017012007286199, 28675043602269632757, 682496208885074229469, 16855397487443215829585, 430393080285140358451479, 11389515859337776256294767
Offset: 1

Views

Author

Antti Karttunen, Dec 20 2015

Keywords

Comments

In factorial base (A007623) these numbers look as:
1, 21, 1011, 21301, 350321, 5300311, 71310201, 905513221, , ...

Crossrefs

Row 1 of A275960.
Binomial transform of A275965 (when both are considered as offset-0 sequences).
Cf. A265908 (first differences), A265905 (variant).
Subsequence of A256450.

Formula

a(1) = 1; for n > 1, a(n) = a(n-1) + A255411(a(n-1)).

Extensions

Note about binomial transform corrected - Antti Karttunen, Sep 20 2016
Showing 1-3 of 3 results.