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A047862 a(n) = T(5,n), array T given by A047858. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 20 06:37 EDT 2022. Contains 353852 sequences. (Running on oeis4.)