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.

Previous Showing 51-52 of 52 results.

A349118 Row sums of a triangle based on A261327.

Original entry on oeis.org

1, 5, 3, 18, 8, 47, 18, 100, 35, 185, 61, 310, 98, 483, 148, 712, 213, 1005, 295, 1370, 396, 1815, 518, 2348, 663, 2977, 833, 3710, 1030, 4555, 1256, 5520, 1513, 6613, 1803, 7842, 2128, 9215, 2490, 10740, 2891, 12425, 3333, 14278, 3818, 16307, 4348, 18520, 4925
Offset: 2

Views

Author

Paul Curtz, Nov 08 2021

Keywords

Comments

The following triangle has A261327 as its diagonals:
1
5
1 2
5 13
1 2 5
5 13 29
1 2 5 10
5 13 29 53
1 2 5 10 17
5 13 29 53 85
...
a(0) = a(1) = 0.
a(n)'s final digit: neither 4 nor 9.
First full bisection difference table:
0, 1, 3, 8, 18, 35, 61, 98, ... = 0, A081489 = b(n)
1, 2, 5, 10, 17, 26, 37, 50, ... = A002522
1, 3, 5, 7, 9, 11, 13, 15, ... = A005408
2, 2, 2, 2, 2, 2, 2, 2, ... = A007395
0, 0, 0, 0, 0, 0, 0, 0, ... = A000004
Second full bisection difference table:
0, 5, 18, 47, 100, 185, 310, 483, ... = c(n)
5, 13, 29, 53, 85, 125, 173, 229, ... = A078370
8, 16, 24, 32, 40, 48, 56, 64, ... = A008590(n+1)
8, 8, 8, 8, 8, 8, 8, 8, ... = A010731
0, 0, 0, 0, 0, 0, 0, 0, ... = A000004
Both bisections are cubic polynomials.
c(-n) = -c(n).

Links

Crossrefs

Cf. A002522, A005408, A007395, A078370, A081489 (first bisection).
Cf. also A008590, A010731, A261327.

Programs

  • Mathematica
    LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {1, 5, 3, 18, 8, 47, 18, 100}, 50] (* Amiram Eldar, Nov 08 2021 *)

Formula

G.f.: (5*x^5+2*x^4-2*x^3-x^2+5*x+1)/((x-1)^4*(x+1)^4).

A349803 a(3*n) = 1 + 4*n^2, a(1+3*n) = 2 + 4*n*(n+1), a(2+3*n) = 5 + 4*n*(n+1).

Original entry on oeis.org

1, 2, 5, 5, 10, 13, 17, 26, 29, 37, 50, 53, 65, 82, 85, 101, 122, 125, 145, 170, 173, 197, 226, 229, 257, 290, 293, 325, 362, 365, 401, 442, 445, 485, 530, 533, 577, 626, 629, 677, 730, 733, 785, 842, 845, 901, 962
Offset: 0

Views

Author

Paul Curtz, Dec 01 2021

Keywords

Comments

A261327 sorted in nondecreasing order.

Links

Crossrefs

Cf. A261327.
Trisections: A053755, A069894, A078370.
Cf. A004396, A004523, A099838.

Programs

  • Mathematica
    nterms=100;LinearRecurrence[{1,0,2,-2,0,-1,1},{1,2,5,5,10,13,17},nterms] (* Paolo Xausa, Dec 01 2021 *)

Formula

a(-n) = a(n) - A099838(n+2).
a(n) = a(n-3) + 4*A004523(n-1) for n >= 3
= a(n-6) + 8*A004396(n-3) for n >= 6
= a(n-9) + 12*A004523(n-4) for n >= 9
= a(n-12) + 16*A004396(n-6) for n >= 12
...
Previous Showing 51-52 of 52 results.

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

Content is available under The OEIS End-User License Agreement.