A213769 Principal diagonal of the convolution array A213768.

1, 8, 26, 63, 136, 272, 521, 968, 1762, 3159, 5600, 9840, 17169, 29784, 51418, 88399, 151432, 258592, 440345, 747960, 1267586, 2143783, 3618816, 6098208, 10260001, 17236712, 28918106, 48454623, 81093832, 135569264, 226404905

Offset: 1

Author

Clark Kimberling, Jun 21 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,4,0,-1).

Crossrefs

Cf. A213768, A213500.

Programs

Mathematica

(See A213768.)
LinearRecurrence[{4,-4,-2,4,0,-1},{1,8,26,63,136,272},40] (* Harvey P. Dale, Jan 08 2015 *)

Formula

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

G.f.: f(x)/g(x), where f(x) = x*(1 + 4*x - 2*x^2 - 7*x^3) and g(x) = (1 - 2*x + x^3 )^2.