A215052 -id:A215052 - cp's OEIS frontend

A036837 Schoenheim bound L_1(n,n-5,n-6).

4, 11, 25, 50, 92, 158, 257, 400, 600, 873, 1237, 1713, 2325, 3100, 4069, 5266, 6729, 8500, 10625, 13155, 16145, 19655, 23750, 28500, 33981, 40274, 47466, 55650, 64925, 75397, 87178, 100387, 115150, 131600, 149878, 170132, 192518

Offset: 7

N. J. A. Sloane, Jan 11 2002

nonn

Mathar observes that this sequence is possibly the same as A215052. - Peter Bala, Mar 29 2014

W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of Jeffrey H. Dinitz and D. R. Stinson, editors, Contemporary Design Theory, Wiley, 1992. See Eq. 1.

Index entries for covering numbers

A column of A036838. A215052.

Conjecture: G.f.: x^7*(4-x^9+5*x^8-10*x^7+10*x^6-5*x^5+2*x^4-5*x^3+10*x^2-9*x) / ((x^4+x^3+x^2+x+1)*(x-1)^6). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009

A215054 a(n) = 1/11*(binomial(n,11) - floor(n/11)).

Original entry on oeis.org

1, 7, 33, 124, 397, 1125, 2893, 6871, 15269, 32065, 64130, 122916, 226922, 405218, 702378, 1185263, 1952198, 3145208, 4966118, 7697483, 11729498, 17594247, 26008887, 37929627, 54618663, 77726559, 109392935, 152368731, 210163767, 287223815, 389141943

Offset: 12

Peter Bala, Aug 01 2012

Let p be a prime. Saikia and Vogrinc have proved that 1/p*{binomial(n,p) - floor(n/p)} is an integer sequence. The present sequence is the case p = 11. Other cases are A002620 (p = 2), A014125 (p = 3), A215052 (p = 5) and A215053 (p = 7).

M. P. Saikia and J. Vogrinc, A simple number theoretic result arxiv.1207.6707v1 [mathNT]
Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 2, -11, 55, -165, 330, -462, 462, -330, 165, -55, 11, -1).

A002620 (p = 2), A014125 (p = 3), A178904, A215052 (p = 5), A215053(p = 7).

Partial sums of A032169.

Table[(Binomial[n,11]-Floor[n/11])/11,{n,12,50}] (* Harvey P. Dale, Aug 06 2012 *)

A215054(n):=1/11*(binomial(n,11) - floor(n/11))$ makelist(A215054(n),n,12,30); /* Martin Ettl, Oct 25 2012 */

a(n) = 1/11*(binomial(n,11) - floor(n/11)).

O.g.f.: sum_{n>=0} a(n)*x^n = x^12*(1 - 4*x + 11*x^2 - 19*x^3 + 23*x^4 - 19*x^5 + 11*x^6 - 4*x^7 + x^8)/((1-x^11)*(1-x)^11) = x^12*(1 + 7*x + 33*x^2 + 124*x^3 + ...). The numerator polynomial 1 - 4*x + 11*x^2 - 19*x^3 + 23*x^4 - 19*x^5 + 11*x^6 - 4*x^7 + x^8 is the negative of the row generating polynomial for row 11 of A178904.

A215053 a(n) = 1/7*( binomial(n,7) - floor(n/7) ).

Original entry on oeis.org

1, 5, 17, 47, 113, 245, 490, 919, 1634, 2778, 4546, 7198, 11074, 16611, 24363, 35022, 49443, 68671, 93971, 126861, 169148, 222968, 290828, 375653, 480836, 610292, 768516, 960645, 1192525, 1470781, 1802893, 2197276, 2663365, 3211705, 3854046

Offset: 8

Peter Bala, Aug 01 2012

Not the same as A011853.

Let p be a prime. Saikia and Vogrinc have proved that 1/p*{binomial(n,p) - floor(n/p)} is an integer sequence. The present sequence is the case p = 7. Other cases are A002620 (p = 2), A014125 (p = 3), A215052 (p = 5) and A215054 (p = 11).

Alexandre Laugier and Manjil Saikia, A characterization of a prime p from the binomial coefficient binomial(n,p), arXiv:1209.2373 [math.NT], The Mathematics Student, Vol. 83 (1-4), pp 1-7, 2014
M. P. Saikia and J. Vogrinc, A simple number theoretic result, arXiv:1207.6707v1 [math.NT]
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 2, -7, 21, -35, 35, -21, 7, -1).

Cf. A002620 (p = 2), A014125 (p = 3), A178904, A215052 (p = 5), A215054 (p = 11).

[(Binomial(n, 7)-Floor(n/7))/7: n in [8..50]]; // Vincenzo Librandi, Jun 23 2015

Table[(Binomial[n,7]-Floor[n/7])/7,{n,8,50}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,2,-7,21,-35,35,-21,7,-1},{1,5,17,47,113,245,490,919,1634,2778,4546,7198,11074,16611},40] (* Harvey P. Dale, Dec 23 2014 *)

a(n) = (binomial(n, 7) - n\7) / 7; \\ Michel Marcus, Jan 23 2014

O.g.f.: sum {n>=0} a(n)*x^n = x^8*(1 - 2*x + 3*x^2 - 2*x^3 + x^4)/((1-x^7)*(1-x)^7) = x^8*(1 + 5*x + 17*x^2 + 47*x^3 + ...). The numerator polynomial 1 - 2*x + 3*x^2 - 2*x^3 + x^4 is the negative of the row generating polynomial for row 7 of A178904.

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A036837 Schoenheim bound L_1(n,n-5,n-6).

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A215054 a(n) = 1/11*(binomial(n,11) - floor(n/11)).

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A215053 a(n) = 1/7*( binomial(n,7) - floor(n/7) ).

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