A156928 G.f. of the z^1 coefficients of the FP1 in the second column of the A156921 matrix.

1, 7, 28, 86, 227, 545, 1230, 2664, 5613, 11611, 23728, 48106, 97031, 195077, 391394, 784284, 1570353, 3142815, 6288100, 12579070, 25161451, 50326697, 100657718, 201320336, 402646197, 805298595

Offset: 2

Author

Johannes W. Meijer, Feb 20 2009

Keywords

• easy
• nonn

Comments

Antidiagonal sums of the convolution array A213582. - Clark Kimberling, Jun 19 2012

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Crossrefs

Cf. A156927.

Equals second column of A156921.

Other columns A156929, A156930, A156931.

Programs

GAP

List([2..40], n-> (9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6); # G. C. Greubel, Jul 08 2019

Magma

[(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6: n in [2..40]]; // G. C. Greubel, Jul 08 2019

Mathematica

Table[(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6, {n, 2, 40}] (* Michael De Vlieger, Sep 23 2017 *)

PARI

vector(40, n, n++; (9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6) \\ G. C. Greubel, Jul 08 2019

Sage

[(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6 for n in (2..40)] # G. C. Greubel, Jul 08 2019

Formula

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) + 2.

a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).

a(n) = (9*2^(n+2) - (2*n^3 + 9*n^2 + 25*n + 36))/6.

G.f.: GF3(z;m=1) = z^2*(1+z)/((1-z)^4*(1-2*z)).

a(n) = Sum_{k=1..n+1} Sum_{i=1..n+1} (k-1)^2 * C(n-k+1,i). - Wesley Ivan Hurt, Sep 22 2017

E.g.f.: (36*exp(2*x) - (36 + 36*x + 15*x^2 + 2*x^3)*exp(x))/6. - G. C. Greubel, Jul 08 2019