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 1-7 of 7 results.

A054128 T(n,2), array T as in A054126.

Original entry on oeis.org

2, 7, 24, 68, 171, 398, 880, 1880, 3925, 8070, 16426, 33216, 66887, 134334, 269348, 539512, 1079993, 2161126, 4323582, 8648704, 17299179, 34600382, 69203064, 138408728, 276820381, 553644038, 1107291730, 2214587520
Offset: 2

Views

Author

Clark Kimberling

Keywords

Links

Formula

G.f.: x^2(-x^5+5x^4-10x^3+10x^2-5x+2)/[(1-2x)(1-x)^4].

A054129 T(n,3), array T as in A054126.

Original entry on oeis.org

2, 9, 39, 134, 394, 1040, 2542, 5876, 13039, 28080, 59163, 122694, 251576, 511720, 1035068, 2085640, 4191629, 8409592, 16852833, 33748170, 67549470, 135164720, 270410170, 540918620, 1081955995, 2164054496
Offset: 3

Views

Author

Clark Kimberling

Keywords

Links

Formula

G.f.: x^3(-x^7+7x^6-21x^5+35x^4-35x^3+21x^2-7x+2)/[(1-2x)(1-x)^6].

A054130 T(n,4), array T as in A054126.

Original entry on oeis.org

2, 11, 58, 236, 802, 2396, 6508, 16448, 39331, 90102, 199652, 431128, 912644, 1902808, 3921896, 8014336, 16273829, 32893762, 66268224, 133194248, 267276526, 535737092, 1073034964, 2148105728, 4298841031, 8601047918, 17206367884, 34418115384, 68842955288
Offset: 4

Views

Author

Clark Kimberling

Keywords

Links

Programs

  • PARI
    Vec(x^4*(x-2)*(x^2-x+1)*(x^6-6*x^5+15*x^4-19*x^3+12*x^2-3*x+1)/((x-1)^8*(2*x-1)) + O(x^100)) \\ Colin Barker, Jan 26 2014

Formula

G.f.: x^4*(x-2)*(x^2-x+1)*(x^6-6*x^5+15*x^4-19*x^3+12*x^2-3*x+1) / ((x-1)^8*(2*x-1)). - Colin Barker, Jan 26 2014

Extensions

More terms from Colin Barker, Jan 26 2014

A054131 T(2n,n), array T as in A054126.

Original entry on oeis.org

2, 5, 24, 134, 802, 4960, 31212, 198504, 1271754, 8192780, 53009614, 344213930, 2241814696, 14637778784, 95786210880
Offset: 0

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A054126.

Programs

  • PARI
    a(n) = if(n==0, 2, 2^(n-1) + sum(m=0, n, binomial(3*n,m))) \\ Jianing Song, May 30 2022

Formula

a(n) = A052509(4*n,3*n+1) + A052509(4*n,n) = 2^(n-1) + Sum_{m=0..n} binomial(3*n,m). for n >= 1. - Jianing Song, May 30 2022

A054132 T(2n+1,n), array T as in A054126.

Original entry on oeis.org

3, 13, 68, 394, 2396, 14925, 94248, 600498, 3851012, 24821845, 160646528, 1043245180, 6794418992, 44360061964, 290244849376
Offset: 0

Views

Author

Clark Kimberling

Keywords

Programs

  • PARI
    a(n) = 2^n + sum(m=0, n+1, binomial(3*n+1,m)) \\ Jianing Song, May 30 2022

Formula

a(n) = A052509(4*n+2,3*n+2) + A052509(4*n+2,n+1) = 2^n + Sum_{m=0..n+1} binomial(3*n+1,m). - Jianing Song, May 30 2022

A054133 T(2n-1,n) where T is the array in A054126.

Original entry on oeis.org

2, 7, 39, 236, 1479, 9418, 60492, 390720, 2534115, 16489802, 107594725, 703681448, 4611414244, 30273029080, 199045400424
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A054126.

Programs

  • PARI
    a(n) = if(n==1, 2, 2^(n-2) + sum(m=0, n-1, binomial(3*n-1, m))) \\ Jianing Song, May 30 2022

Formula

a(n) = A052509(4*n-2,3*n) + A052509(4*n-2,n-1) = 2^(n-2) + Sum_{m=0..n-1} binomial(3*n-1,m) for n >= 2. - Jianing Song, May 30 2022

Extensions

Definition clarified by Eric Rowland, May 29 2022

A054127 a(1) = 2; a(n) = 9*2^(n-2) - n - 2, n>1.

Original entry on oeis.org

2, 5, 13, 30, 65, 136, 279, 566, 1141, 2292, 4595, 9202, 18417, 36848, 73711, 147438, 294893, 589804, 1179627, 2359274, 4718569, 9437160, 18874343, 37748710, 75497445, 150994916, 301989859, 603979746, 1207959521
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Second column of A054126.

Links

Crossrefs

Cf. A054126.

Programs

  • Mathematica
    Join[{2},Table[9*2^(n-2)-n-2,{n,2,30}]] (* Harvey P. Dale, Jul 16 2020 *)
LinearRecurrence[{4,-5,2},{2,5,13,30},30] (* Harvey P. Dale, Aug 01 2021 *)

Formula

a(n) = A054126(n, 1).
G.f.: x * (2-x) * (1-x+x^2) / ( (1-x)^2 * (1-2*x) ). - Joerg Arndt, Dec 01 2014
Showing 1-7 of 7 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.