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A096957 Fourth column (m=3) of (1,6)-Pascal triangle A096956. 4
6, 19, 40, 70, 110, 161, 224, 300, 390, 495, 616, 754, 910, 1085, 1280, 1496, 1734, 1995, 2280, 2590, 2926, 3289, 3680, 4100, 4550, 5031, 5544, 6090, 6670, 7285, 7936, 8624, 9350, 10115, 10920, 11766, 12654, 13585, 14560, 15580, 16646, 17759, 18920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If Y is a 6-subset of an n-set X then, for n>=8, a(n-8) is the number of 3-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 16 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = A096956(n+3, 3) = 6*b(n) - 5*b(n-1) = (n+18)*binomial(n+2, 2)/3, with b(n):=A000292(n)=binomial(n+3, 3).

G.f.: (6-5*x)/(1-x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Apr 19 2017

MATHEMATICA

CoefficientList[Series[(6 - 5*x)/(1 - x)^4, {x, 0, 40}], x] (* Wesley Ivan Hurt, Apr 18 2017 *)

LinearRecurrence[{4, -6, 4, -1}, {6, 19, 40, 70}, 50] (* Vincenzo Librandi, Apr 19 2017 *)

PROG

(MAGMA) I:=[6, 19, 40, 70]; [n le 4 select I[n] else 4*Self(n-1)- 6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Apr 19 2017

CROSSREFS

Cf. A056115 (third column), A096958 (fifth column).

Sequence in context: A106398 A179986 A054567 * A272811 A273206 A273394

Adjacent sequences:  A096954 A096955 A096956 * A096958 A096959 A096960

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 13 2004

STATUS

approved

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)