A047862 a(n) = T(5,n), array T given by A047858.

1, 7, 20, 48, 108, 236, 508, 1084, 2300, 4860, 10236, 21500, 45052, 94204, 196604, 409596, 851964, 1769468, 3670012, 7602172, 15728636, 32505852, 67108860, 138412028, 285212668, 587202556, 1207959548, 2483027964, 5100273660, 10468982780, 21474836476

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (6, 7, 8, ...).

More generally the main diagonal of the array defined by T(0,j) = j+1 with j>=0, T(i,0) = i+1 with i>=0, T(i,j) = T(i-1,j-1) + T(i-1,j) + A, is given by T(n,n) = 2^(n-1)*(n+2*A+2)-A. - Benoit Cloitre, Jun 17 2003

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Programs

Magma

[2^(n-1)*(n+10)-4: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011

PARI

Vec((1+2*x-7*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

Formula

From Benoit Cloitre, Jun 17 2003: (Start)

Main diagonal of the array defined by T(0, j) = j+1 with j>=0, T(i, 0) = i+1 with i>=0, T(i,j) = T(i-1,j-1)+T(i-1,j)+ 4. Therefore, for i = j = n:

a(n) = 2^(n-1)*(n+10)-4. (End)

a(0)=1, a(1)=7, a(2)=20; for n>2, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - Vincenzo Librandi, Sep 28 2011

a(n) = 2^(n-1)*(n+10)-4. G.f.: (1+2*x-7*x^2) / ((1-x)*(1-2*x)^2). - Colin Barker, Feb 18 2016