The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A212562 Number of (w,x,y,z) with all terms in {1,...,n} and w+x<2y+2z. 2
 0, 1, 15, 73, 228, 551, 1137, 2097, 3568, 5701, 8675, 12681, 17940, 24683, 33173, 43681, 56512, 71977, 90423, 112201, 137700, 167311, 201465, 240593, 285168, 335661, 392587, 456457, 527828, 607251, 695325, 792641, 899840, 1017553, 1146463, 1287241, 1440612 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For a guide to related sequences, see A211795. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1). FORMULA a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7). From Colin Barker, Dec 05 2015: (Start) a(n) = 1/96*(82*n^4 + 12*n^3 + 8*n^2 + 6*((-1)^n-1)*n - 3*(-1)^n + 3). G.f.: x*(1 + 12*x + 29*x^2 + 29*x^3 + 10*x^4 + x^5) / ((1-x)^5*(1+x)^2). (End) MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w + x < 2 y + 2 z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]] (* A212562 *) CoefficientList[Series[x (1 + 12 x + 29 x^2 + 29 x^3 + 10 x^4 + x^5)/((1 - x)^5 (1 + x)^2), {x, 0, 33}], x] (* Vincenzo Librandi, Dec 05 2015 *) PROG (PARI) concat(0, Vec(x*(1+12*x+29*x^2+29*x^3+10*x^4+x^5)/((1-x)^5*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015 (Magma) I:=[0, 1, 15, 73, 228, 551, 1137]; [n le 7 select I[n] else 3*Self(n-1)-Self(n-2)-5*Self(n-3)+5*Self(n-4)+Self(n-5)-3*Self(n-6)+Self(n-7): n in [1..40]]; // Vincenzo Librandi, Dec 05 2015 CROSSREFS Cf. A211795. Sequence in context: A053531 A000476 A002603 * A212092 A022817 A171341 Adjacent sequences: A212559 A212560 A212561 * A212563 A212564 A212565 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 21 2012 STATUS approved

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

Last modified May 22 10:20 EDT 2024. Contains 372745 sequences. (Running on oeis4.)