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

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,5,-5).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A026386.

Sequence in context: A178941 A178155 A330457 * A176502 A319003 A141199

Adjacent sequences: A026393 A026394 A026395 * A026397 A026398 A026399

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved