A026396 Sum_{T(i,j)}, 0<=j<=i, 0<=i<=n, where T is the array in A026386.

3, 7, 17, 37, 87, 187, 437, 937, 2187, 4687, 10937, 23437, 54687, 117187, 273437, 585937, 1367187, 2929687, 6835937, 14648437, 34179687, 73242187, 170898437, 366210937, 854492187, 1831054687, 4272460937, 9155273437, 21362304687, 45776367187, 106811523437

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,5,-5).

Crossrefs

Cf. A026386.

Programs

Mathematica

LinearRecurrence[{1, 5, -5}, {3, 7, 17}, 50] (* Paolo Xausa, Sep 16 2024 *)

PARI

Vec((-5*x^2 + 4*x + 3)/(5*x^3 - 5*x^2 - x + 1) + O(x^40)) \\ Colin Barker, Nov 25 2016

Formula

G.f.: (3+4*x-5*x^2) / ((1-x)*(1-5*x^2)). - Ralf Stephan, Apr 30 2004

From Colin Barker, Nov 25 2016: (Start)

a(n) = (7*5^(n/2) - 1)/2 for n even.

a(n) = (6*5^((n+1)/2) - 2)/4 for n odd.

a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) for n>2. (End)

a(n) = (3-(-1)^n-(13+(-1)^n)*5^((1-(-1)^n+2*n)/4))/(2*(-1)^n-6). - Wesley Ivan Hurt, Oct 02 2021