This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A306210 T(n,k) = binomial(n + k, n) - binomial(n + floor(k/2), n) + 1, square array read by descending antidiagonals (n >= 0, k >= 0). 0
 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 4, 4, 1, 1, 3, 8, 7, 5, 1, 1, 4, 10, 17, 11, 6, 1, 1, 4, 16, 26, 31, 16, 7, 1, 1, 5, 19, 47, 56, 51, 22, 8, 1, 1, 5, 27, 65, 112, 106, 78, 29, 9, 1, 1, 6, 31, 101, 176, 232, 183, 113, 37, 10, 1, 1, 6, 41, 131, 296, 407, 435, 295, 157, 46, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS There are at most T(n,k) possible values for the number of knots in an interpolatory cubature formula of degree k for an integral over an n-dimensional region. LINKS Ronald Cools, Encyclopaedia of Cubature Formulas Ronald Cools, A Survey of Methods for Constructing Cubature Formulae, In: Espelid T.O., Genz A. (eds), Numerical Integration, NATO ASI Series (Series C: Mathematical and Physical Sciences), Vol. 357, 1991, Springer, Dordrecht, pp. 1-24. T. N. L. Patterson, On the Construction of a Practical Ermakov-Zolotukhin Multiple Integrator, In: Keast P., Fairweather G. (eds), Numerical Integration, NATO ASI Series (Series C: Mathematical and Physical Sciences), Vol. 203, 1987, Springer, Dordrecht, pp. 269-290. FORMULA T(n,k) = A007318(n+k,n) - A046854(n+k,n) + 1. G.f.: (1 - x - x^2 + x^3 - 2*y + 2*x*y + y^2 - x*y^2 + x^2*y^2)/((1 - x)*(1 - y)*(1 - x - y)*(1 - x^2 - y)). EXAMPLE Square array begins:   1, 1,  1,   1,   1,    1,    1,    1,     1,  ...   1, 2,  2,   3,   3,    4,    4,    5,     5,  ...   1, 3,  4,   8,  10,   16,   19,   27,    31,  ...   1, 4,  7,  17,  26,   47,   65,  101,   131,  ...   1, 5, 11,  31,  56,  112,  176,  296,   426,  ...   1, 6, 16,  51, 106,  232,  407,  737,  1162,  ...   1, 7, 22,  78, 183,  435,  841, 1633,  2794,  ...   1, 8, 29, 113, 295,  757, 1597, 3313,  6106,  ...   1, 9, 37, 157, 451, 1243, 2839, 6271, 12376,  ...   ... As triangular array, this begins:   1;   1, 1;   1, 2,  1;   1, 2,  3,  1;   1, 3,  4,  4,  1;   1, 3,  8,  7,  5,  1;   1, 4, 10, 17, 11,  6,  1;   1, 4, 16, 26, 31, 16,  7, 1;   1, 5, 19, 47, 56, 51, 22, 8, 1;   ... MATHEMATICA T[n_, k_] = Binomial[n + k, n] - Binomial[n + Floor[k/2], n] + 1; Table[T[k, n - k], {k, 0, n}, {n, 0, 20}] // Flatten PROG (Maxima) T(n, k) := binomial(n + k, n) - binomial(n + floor(k/2), n) + 1\$ create_list(T(k, n - k), n, 0, 20, k, 0, n); CROSSREFS Cf. A007318, A046854, A322596. Sequence in context: A202176 A168443 A156041 * A133255 A282748 A145972 Adjacent sequences:  A306207 A306208 A306209 * A306211 A306212 A306213 KEYWORD nonn,easy,tabl AUTHOR Franck Maminirina Ramaharo, Jan 29 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)