A095694 T(n,3) diagonal of triangle in A095693.

1, 22, 130, 485, 1400, 3416, 7392, 14610, 26895, 46750, 77506, 123487, 190190, 284480, 414800, 591396, 826557, 1134870, 1533490, 2042425, 2684836, 3487352, 4480400, 5698550, 7180875, 8971326, 11119122, 13679155, 16712410, 20286400, 24475616, 29361992, 35035385, 41594070, 49145250

Offset: 2

Author

Nicholas S. Horne (nickhorne(AT)cox.net), Jul 06 2004

Keywords

• easy
• nonn

References

• Nicholas S. Horne, Analysis of Viable Network Configurations from a Combinatorial, Graphical and Algebraic Perspective, Diss. Providence College, 2004.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A095693.

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,22,130,485,1400,3416,7392},30] (* Harvey P. Dale, Jul 10 2021 *)

Formula

a(n) = (n + 1)*n*(n - 1)*(n^3 + 3*n^2 + 2*n - 16)/48. - corrected by Eric Rowland, Aug 15 2017

G.f.: x^2*(2*x^3-3*x^2+15*x+1)/(1-x)^7. - Colin Barker, Nov 24 2012

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Wesley Ivan Hurt, Apr 12 2023