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A095668 Sixth column (m=5) of (1,4)-Pascal triangle A095666. 1
4, 21, 66, 161, 336, 630, 1092, 1782, 2772, 4147, 6006, 8463, 11648, 15708, 20808, 27132, 34884, 44289, 55594, 69069, 85008, 103730, 125580, 150930, 180180, 213759, 252126, 295771, 345216, 401016, 463760, 534072, 612612, 700077, 797202, 904761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If Y is a 4-subset of an n-set X, then, for n >= 8, a(n-8) is the number of 5-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 (6,-15,20,-15,6,-1).

FORMULA

G.f.: (4-3*x)/(1-x)^6.

a(n) = (n+20)*binomial(n+4, 4)/5.

a(n) = 4*b(n) - 3*b(n-1), with b(n) = binomial(n+5, 5) = A000389(n+5, 5).

E.g.f.: (480 + 2040*x + 1680*x^2 + 440*x^3 + 40*x^4 + x^5)*exp(x)/120. - G. C. Greubel, Nov 25 2017

a(n) = Sum_{i=0..n+1} A000217(i)*A055999(n+2-i). - Bruno Berselli, Mar 05 2018

MAPLE

A095668:=n->(n+20)*binomial(n+4, 4)/5: seq(A095668(n), n=0..80); # Wesley Ivan Hurt, Nov 25 2017

MATHEMATICA

Table[(n + 20)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* G. C. Greubel, Nov 25 2017 *)

PROG

(PARI) for(n=0, 30, print1((n+20)*binomial(n+4, 4)/5, ", ")) \\ G. C. Greubel, Nov 25 2017

(MAGMA) [(n+20)*Binomial(n+4, 4)/5: n in [0..30]]; // G. C. Greubel, Nov 25 2017

CROSSREFS

Cf. A000389, A095666.

Cf. A000217, A055999.

Sequence in context: A131478 A089893 A212246 * A078800 A184706 A034960

Adjacent sequences:  A095665 A095666 A095667 * A095669 A095670 A095671

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 11 2004

STATUS

approved

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Last modified May 18 00:43 EDT 2021. Contains 343992 sequences. (Running on oeis4.)