A213763 Principal diagonal of the convolution array A213762.

1, 11, 43, 127, 331, 807, 1891, 4319, 9691, 21463, 47059, 102351, 221131, 475079, 1015747, 2162623, 4587451, 9699255, 20447155, 42991535, 90177451, 188743591, 394264483, 822083487, 1711275931, 3556769687, 7381974931

Offset

1,2

Comments

Create a triangle with first column T(n,1)=1+4*n for n=0,1,2... The remaining terms T(r,c)=T(r,c-1)+T(r-1,c-1). The sum of the terms in row(n)=a(n+1). - J. M. Bergot, Dec 18 2012

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Formula

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

a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).

G.f.: x*(1 + 5*x - 10*x^2)/(1 - 3*x + 2*x^2 )^2.

Mathematica

(See A213762.)
LinearRecurrence[{6, -13, 12, -4}, {1, 11, 43, 127}, 30] (* Harvey P. Dale, Apr 13 2017 *)

Crossrefs

Cf. A213762, A213500.

Sequence in context: A352966 A142039 A196153 * A302226 A201714 A269422

Adjacent sequences: A213760 A213761 A213762 * A213764 A213765 A213766

Keyword

nonn,easy

Author

Clark Kimberling, Jun 20 2012

Status

approved