A213754 Principal diagonal of the convolution array A213753.

1, 16, 111, 576, 2631, 11292, 46927, 191680, 775599, 3122076, 12531591, 50220912, 201088855, 804798268, 3220143903, 12882607872, 51534757599, 206148206268, 824612224663, 3298489794160, 13194045161031, 52776361000476

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-47,101,-116,68,-16).

Formula

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

a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) - 16*a(n-6) for n>5. Corrected by Colin Barker, Nov 07 2017

G.f.: f(x)/g(x), where f(x) = x*(1 + 5*x - 18*x^2 + 6*x^3 + 12*x^4) and g(x) = (1 - 4*x) * (1 - x)^3 * (1 - 2*x)^2.

Mathematica

(See A213753.)

Prog

(PARI) Vec(x*(1 + 5*x - 18*x^2 + 6*x^3 + 12*x^4) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Nov 07 2017

Crossrefs

Cf. A213753, A213500.

Sequence in context: A177046 A234250 A240786 * A371114 A279425 A144449

Adjacent sequences: A213751 A213752 A213753 * A213755 A213756 A213757

Keyword

nonn,easy

Author

Clark Kimberling, Jun 20 2012

Status

approved