A350292 -id:A350292 - cp's OEIS frontend

A350295 2nd subdiagonal of the triangle A350292.

6, 8, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540

Offset: 3

Stefano Spezia, Dec 23 2021

Harvey P. Dale, Table of n, a(n) for n = 3..1000
Heiko Harborth and Hauke Nienborg, Saturated vertex Turán numbers for cube graphs, Congr. Num. 208 (2011), 183-188.
Mathonline, Cube Graphs
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000217, A112355, A161680, A350292.

Join[{6,8},Table[Binomial[n,2],{n,5,56}]]
LinearRecurrence[{3,-3,1},{6,8,10,15,21},60] (* Harvey P. Dale, Jul 01 2022 *)

a(n) = binomial(n, 2) = A000217(n-1) for n > 4 with a(3) = 6 and a(4) = 8 (see Theorem 3 in Harborth and Nienborg).
O.g.f.: x^3*(2*x^4 - 3*x^3 - 4*x^2 + 10*x - 6)/(x - 1)^3.
E.g.f.: x^2*(x^2 + 6*x + 6*exp(x) - 6)/12.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 7.

A350293 a(n) is the 1st saturated vertex Turán number for the cube graph Q_n.

Original entry on oeis.org

1, 2, 6, 12, 24, 52, 112

Offset: 1

Stefano Spezia, Dec 23 2021

The 1st saturated vertex Turán number for the cube graph Q_n is the maximum number of vertices to be deleted from the cube graph such that no subgraph Q_1 is complete and each of the deleted vertices being added again completes a subgraph Q_1 (see Harborth and Nienborg).

Heiko Harborth and Hauke Nienborg, Saturated vertex Turán numbers for cube graphs, Congr. Num. 208 (2011), 183-188.
Mathonline, Cube Graphs

First column of A350292.

Cf. A000225, A350294.

a(n) = n*2^n/(n + 1) iff n is a Mersenne number (see Theorem 1 in Harborth and Nienborg).

a(n) <= A350294(n) (see Lemma 1 in Harborth and Nienborg).

cp's OEIS Frontend

A350295 2nd subdiagonal of the triangle A350292.

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