A095670 Eighth column (m=7) of (1,4)-Pascal triangle A095666.

4, 29, 120, 372, 960, 2178, 4488, 8580, 15444, 26455, 43472, 68952, 106080, 158916, 232560, 333336, 468996, 648945, 884488, 1189100, 1578720, 2072070, 2691000, 3460860, 4410900, 5574699, 6990624, 8702320, 10759232, 13217160, 16138848, 19594608, 23662980, 28431429

Offset

0,1

Comments

If Y is a 4-subset of an n-set X then, for n >= 10, a(n-10) is the number of 7-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: (4-3*x)/(1-x)^8.

a(n) = 4*b(n) - 3*b(n-1) = (n+28)*binomial(n+6, 6)/7, with b(n) = binomial(n+7, 7) = A000580(n+7, 7).

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 1010432020569997/3396225623076000.

Sum_{n>=0} (-1)^n/a(n) = 56896*log(2)/1035 - 128655075588919507/3396225623076000. (End)

E.g.f.: (1/7!)*(20160 + 126000*x + 166320*x^2 + 79800*x^3 + 16800*x^4 + 1638*x^5 + 70*x^6 + x^7)*exp(x). - G. C. Greubel, Nov 15 2025

Mathematica

a[n_] := (n+28) * Binomial[n+6, 6]/7; Array[a, 30, 0] (* Amiram Eldar, Oct 21 2025 *)

Prog

(Magma)
A095670:= func< n | (n+28)*Binomial(n+6, 6)/7 >;
[A095670(n): n in [0..40]]; // G. C. Greubel, Nov 15 2025
(SageMath)
def A095670(n): return (n+28)*binomial(n+6, 6)//7
print([A095670(n) for n in range(41)]) # G. C. Greubel, Nov 15 2025

Crossrefs

Cf. A000580, A095666.

Sequence in context: A345897 A368372 A372424 * A370435 A353972 A273074

Adjacent sequences: A095667 A095668 A095669 * A095671 A095672 A095673

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved