A011847 -id:A011847 - cp's OEIS frontend

A011846 a(n) = floor( binomial(n,9)/10 ).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 22, 71, 200, 500, 1144, 2431, 4862, 9237, 16796, 29393, 49742, 81719, 130750, 204297, 312455, 468682, 690690, 1001500, 1430715, 2016007, 2804880, 3856710, 5245125, 7060746

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, order 259.

A column of triangle A011847.

[Floor(Binomial(n,9)/10): n in [0..50]]; // Vincenzo Librandi, Apr 11 2017

A011846:=n->floor(binomial(n,9)/10): seq(A011846(n), n=0..60); # Wesley Ivan Hurt, Apr 10 2017

Table[Floor[Binomial[n, 9]/10], {n, 0, 50}] (* Vincenzo Librandi, Apr 11 2017 *)

a(n) = floor( binomial(n+1,10)/(n+1)). [Gary Detlefs, Nov 23 2011]

A095719 a(n) = Sum_{k = 0..floor(n/2)} floor(C(n-k,k)/(k+1)).

Original entry on oeis.org

1, 1, 2, 2, 4, 5, 8, 11, 18, 25, 40, 59, 90, 137, 210, 319, 492, 754, 1164, 1798, 2786, 4317, 6710, 10438, 16266, 25377, 39650, 62013, 97108, 152212, 238822, 375058, 589520, 927365, 1459960, 2300097, 3626211, 5720649, 9030450, 14263675

Offset: 1

Mike Zabrocki, Jul 08 2004

nonn

Sums of diagonal entries in A011847.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A011847, A095718.

A095719:= func< n | (&+[Floor(Binomial(n-k,k)/(k+1)): k in [0..Floor(n/2)]]) >;
[A095719(n): n in [1..40]]; // G. C. Greubel, Oct 21 2024

a:=n->add(floor(C(n-k,k)/(k+1)),k=0..n/2);

Table[Sum[Floor[Binomial[n-k,k]/(k+1)],{k,0,n/2}],{n,40}] (* Harvey P. Dale, Apr 02 2019 *)

def A095719(n): return sum(binomial(n-k,k)//(k+1) for k in range(n//2+1))
[A095719(n) for n in range(1,41)] # G. C. Greubel, Oct 21 2024

a(n) = Sum_{k=0..floor(n/2)} floor(C(n-k,k)/(k+1)).

A011843 a(n) = floor(binomial(n,5)/6).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 9, 21, 42, 77, 132, 214, 333, 500, 728, 1031, 1428, 1938, 2584, 3391, 4389, 5608, 7084, 8855, 10963, 13455, 16380, 19792, 23751, 28318, 33562, 39556, 46376, 54105, 62832, 72649, 83657

Offset: 0

N. J. A. Sloane

nonn

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 5, -10, 10, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1).

A column of triangle A011847.

seq(floor(binomial(n,5)/6), n=0..38); # Zerinvary Lajos, Jan 12 2009

a(n) = +5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) +a(n-18) -5*a(n-19) +10*a(n-20) -10*a(n-21) +5*a(n-22) -a(n-23) -a(n-36) +5*a(n-37) -10*a(n-38) +10*a(n-39) -5*a(n-40) +a(n-41) +a(n-54) -5*a(n-55) +10*a(n-56) -10*a(n-57) +5*a(n-58) -a(n-59). [R. J. Mathar, Apr 15 2010]

a(n) = floor(binomial(n+1,6)/(n+1)). [Gary Detlefs, Nov 23 2011]

A011844 a(n) = floor(C(n,7)/8).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 15, 41, 99, 214, 429, 804, 1430, 2431, 3978, 6298, 9690, 14535, 21318, 30644, 43263, 60087, 82225, 111003, 148005, 195097, 254475, 328696, 420732, 534006, 672452, 840565, 1043460

Offset: 0

N. J. A. Sloane

nonn

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -7, 21, -35, 35, -21, 7, -1).

A column of triangle A011847.

Floor[Binomial[Range[0,40],7]/8] (* Harvey P. Dale, Apr 23 2011 *)

a(n) = floor(binomial(n+1,8)/(n+1)). [Gary Detlefs, Nov 23 2011]

cp's OEIS Frontend

A011846 a(n) = floor( binomial(n,9)/10 ).

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A095719 a(n) = Sum_{k = 0..floor(n/2)} floor(C(n-k,k)/(k+1)).

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A011843 a(n) = floor(binomial(n,5)/6).

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A011844 a(n) = floor(C(n,7)/8).

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