A095669 Seventh column (m=6) of (1,4)-Pascal triangle A095666.

4, 25, 91, 252, 588, 1218, 2310, 4092, 6864, 11011, 17017, 25480, 37128, 52836, 73644, 100776, 135660, 179949, 235543, 304612, 389620, 493350, 618930, 769860, 950040, 1163799, 1415925, 1711696, 2056912, 2457928, 2921688, 3455760, 4068372, 4768449, 5565651, 6470412

Offset

0,1

Comments

If Y is a 4-subset of an n-set X then, for n >= 9, a(n-9) is the number of 6-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 (7,-21,35,-35,21,-7,1).

Formula

G.f.: (4-3*x)/(1-x)^7.

a(n) = 4*b(n) - 3*b(n-1) = (n+24)*binomial(n+5, 5)/6, with b(n) = binomial(n+6, 6) = A000579(n+6, 6).

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 617753422765/2001827195368.

Sum_{n>=0} (-1)^n/a(n) = 70080*log(2)/3059 - 470272440453461/30027407930520. (End)

E.g.f.: (1/6!)*(2880 + 15120*x + 16200*x^2 + 6000*x^3 + 900*x^4 + 54*x^5 + x^6)*exp(x). - G. C. Greubel, Nov 15 2025

Mathematica

a[n_] := (n+24) * Binomial[n+5, 5]/6; Array[a, 30, 0] (* Amiram Eldar, Oct 21 2025 *)

Prog

(Magma)
A095669:= func< n | (n+24)*Binomial(n+5, 5)/6 >;
[A095669(n): n in [0..40]]; // G. C. Greubel, Nov 15 2025
(SageMath)
def A095669(n): return (n+24)*binomial(n+5, 5)//6
print([A095669(n) for n in range(41)]) # G. C. Greubel, Nov 15 2025
(PARI) a(n) = (n+24)*binomial(n+5, 5)/6 \\ Bruce Nye, Feb 19 2026

Crossrefs

Cf. A000579, A095666.

Sequence in context: A303514 A041991 A027764 * A323967 A195509 A027949

Adjacent sequences: A095666 A095667 A095668 * A095670 A095671 A095672

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved