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.

A359620 Number of edge cuts in the n-antiprism graph.

Original entry on oeis.org

1, 4, 62, 1440, 30346, 589556, 10858046, 192811016, 3336192082, 56642890908, 948242161382, 15706527467824, 258068117928826, 4214126476848580, 68489478048350222, 1109069751830483544, 17909240724783047842, 288575383662532867820, 4642173797092097149238
Offset: 0

Views

Author

Eric W. Weisstein, Jan 07 2023

Keywords

Comments

The n-antiprism graph is defined for n >= 3. The sequence has been extrapolated to n = 0 using the recurrence. - Andrew Howroyd, Jan 26 2023

Links

Crossrefs

Cf. A359621.

Programs

  • Mathematica
    Table[2 + 16^n - 2^(n + 1) ChebyshevT[n, 3] + (6 - 2^(n + 1) (Fibonacci[2 n, 2] + 3 Fibonacci[2 n - 1, 2])) n/7, {n, 10}] // Expand (* Eric W. Weisstein, Mar 07 2023 *)
LinearRecurrence[{42, -617, 3640, -7144, 5888, -2064, 256}, {1, 4, 62, 1440, 30346, 589556, 10858046}, 20] (* Eric W. Weisstein, Mar 07 2023 *)
CoefficientList[Series[-(1 - 38 x + 511 x^2 - 2336 x^3 + 704 x^4 + 512 x^5 + 16 x^6)/((-1 + x)^2 (-1 + 16 x) (1 - 12 x + 4 x^2)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)
  • PARI
    Vec((1 - 38*x + 511*x^2 - 2336*x^3 + 704*x^4 + 512*x^5 + 16*x^6)/((1 - x)^2*(1 - 16*x)*(1 - 12*x + 4*x^2)^2) + O(x^21)) \\ Andrew Howroyd, Jan 26 2023

Formula

G.f.: (1 - 38*x + 511*x^2 - 2336*x^3 + 704*x^4 + 512*x^5 + 16*x^6)/((1 - x)^2*(1 - 16*x)*(1 - 12*x + 4*x^2)^2). - Andrew Howroyd, Jan 26 2023
a(n) = 42*a(n-1) - 617*a(n-2) + 3640*a(n-3) - 7144*a(n-4) + 5888*a(n-5) - 2064*a(n-6) + 256*a(n-7). - Wesley Ivan Hurt, May 24 2024

Extensions

a(0)-(2) prepended and terms a(7) and beyond from Andrew Howroyd, Jan 26 2023

A359987 Number of edge cuts in the n-ladder graph P_2 X P_n.

Original entry on oeis.org

1, 11, 105, 919, 7713, 63351, 514321, 4148839, 33347041, 267489431, 2143168305, 17160184519, 137349160833, 1099102033911, 8794224638161, 70360221445159, 562911076526881, 4503422288363351, 36027988077717105, 288226686123491719, 2305826176955087553, 18446667292472959671
Offset: 1

Views

Author

Andrew Howroyd, Jan 28 2023

Keywords

Links

Crossrefs

Row 2 of A359990.
Cf. A013730, A107839, A356828 (vertex cuts), A359989.
Cf. A359621, A359622.

Programs

  • Mathematica
    LinearRecurrence[{13, -42, 16}, {1, 11, 105}, 25] (* Paolo Xausa, Jun 24 2024 *)
Table[2^(3 n - 2) + (((5 - Sqrt[17])/2)^n - ((5 + Sqrt[17])/2)^n)/Sqrt[17], {n, 20}] // Expand (* Eric W. Weisstein, Nov 03 2024 *)
CoefficientList[Series[-(1 - 2 x + 4 x^2)/((-1 + 8 x) (1 - 5 x + 2 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 03 2024 *)
  • PARI
    Vec((1 - 2*x + 4*x^2)/((1 - 8*x)*(1 - 5*x + 2*x^2)) + O(x^25))

Formula

a(n) = 13*a(n-1) - 42*a(n-2) + 16*a(n-3) for n > 3.
a(n) = A013730(n-1) - A107839(n-1).
G.f.: x*(1 - 2*x + 4*x^2)/((1 - 8*x)*(1 - 5*x + 2*x^2)).

A377773 Number of edge cuts in the n-web graph.

Original entry on oeis.org

1, 12, 223, 3898, 64453, 1042868, 16747743, 268285422, 4294211881, 68715706984, 1099492954547, 17592094126818, 281474526684989, 4503597434338652, 72057583394694855, 1152921453139596758, 18446743825630274641, 295147903987017778256, 4722366477153821698011
Offset: 0

Views

Author

Eric W. Weisstein, Nov 06 2024

Keywords

Comments

Extended to a(0) using the formula/recurrence. - Eric W. Weisstein, Dec 01 2024

Links

Crossrefs

Cf. A359621.

Programs

  • Magma
    I:=[1, 12, 223, 3898, 64453, 1042868, 16747743]; [n le 7 select I[n] else 28*Self(n-1)-242*Self(n-2)+888*Self(n-3)-1481*Self(n-4)+1196*Self(n-5)-452*Self(n-6)+64*Self(n-7): n in [1..40]]; // Vincenzo Librandi, Jan 02 2025
  • Mathematica
    LinearRecurrence[{28, -242, 888, -1481, 1196, -452, 64}, {1, 12, 223, 3898, 64453, 1042868, 16747743}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 - 16 x + 129 x^2 - 330 x^3 + 100 x^4 + 52 x^5 + 4 x^6)/((-1 + x)^2 (-1 + 16 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

Formula

a(n) = 16^n - 8^n + A359621(n). - Christian Sievers, Nov 21 2024
a(n) = 28*a(n-1)-242*a(n-2)+888*a(n-3)-1481*a(n-4)+1196*a(n-5)-452*a(n-6)+64*a(n-7). - Eric W. Weisstein, Dec 01 2024
G.f.: -(1-16*x+129*x^2-330*x^3+100*x^4+52*x^5+4*x^6)/((-1+x)^2*(-1+16*x)*(1-5*x+2*x^2)^2). - Eric W. Weisstein, Dec 01 2024

Extensions

a(8) and beyond from Christian Sievers, Nov 21 2024
Showing 1-3 of 3 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.