OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (165,-9225,237297,-3097935,21760767,-83084547, 168886683,-184022244,101917648,-22588608).
FORMULA
a(n) = 84^n - (6*n + 1)*28^n + binomial(6*n+1, 2)*7^n - binomial(6*n+1, 3). - Andrew Howroyd, May 07 2020
From G. C. Greubel, Sep 12 2022: (Start)
a(n) = Sum_{j=0..3} (-1)^j*binomial(6*n+1, j)*binomial(9-j, 6)^n.
G.f.: 4*x^2*(100 + 41825*x + 83559*x^2 - 21052241*x^3 + 67903073*x^4 + 129637536*x^5 - 671540492*x^6 - 210827008*x^7)/( Product_{j=0..3} (1 - binomial(j+6, 6)*x)^(4-j) ).
E.g.f.: exp(84*x) - (1 + 168*x)*exp(28*x) + 147*x*(1 + 6*x)*exp(7*x) - x*(35 + 108*x + 36*x^2)*exp(x). (End)
MATHEMATICA
Table[Sum[(-1)^j*Binomial[6*n+1, j]*Binomial[9-j, 6]^n, {j, 0, 3}], {n, 30}] (* G. C. Greubel, Sep 12 2022 *)
PROG
(PARI) a(n) = {84^n - (6*n + 1)*28^n + binomial(6*n+1, 2)*7^n - binomial(6*n+1, 3)} \\ Andrew Howroyd, May 07 2020
(Magma) [(&+[(-1)^j*Binomial(6*n+1, j)*Binomial(9-j, 6)^n: j in [0..3]]): n in [1..30]]; // G. C. Greubel, Sep 12 2022
(SageMath)
def A151652(n): return sum((-1)^j*binomial(6*n+1, j)*binomial(9-j, 6)^n for j in (0..3))
[A151652(n) for n in (1..30)] # G. C. Greubel, Sep 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 29 2009
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, May 07 2020
STATUS
approved