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

0,2

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).

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

Prog

(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

Crossrefs

Sequence in context: A298288 A299384 A007044 * A264879 A320681 A048755

Adjacent sequences: A047859 A047860 A047861 * A047863 A047864 A047865

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved