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

Author

Stefano Spezia, Dec 23 2021

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A000217, A112355, A161680, A350292.

Programs

Mathematica

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 *)

Formula

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.