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

Author

Clark Kimberling, Jun 20 2012

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A213762, A213500.

Programs

Mathematica

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

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.