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 A212967 Number of (w,x,y) with all terms in {0,...,n} and w < range{w,x,y}. 3
 0, 3, 10, 26, 50, 89, 140, 212, 300, 415, 550, 718, 910, 1141, 1400, 1704, 2040, 2427, 2850, 3330, 3850, 4433, 5060, 5756, 6500, 7319, 8190, 9142, 10150, 11245, 12400, 13648, 14960, 16371, 17850, 19434, 21090, 22857, 24700, 26660, 28700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For a guide to related sequences, see A212959. LINKS Muniru A Asiru, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA a(n) + A212968(n) = (n + 1)^3. a(n) = (n + 1)*(10*n*(n + 2) - 3*(-1)^n + 3)/24. a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6). G.f.: f(x)/g(x), where f(x) = x*(3 + 4*x + 3*x^2) and g(x) = ((1 - x)^4)(1 + x)^2. a(n) = Sum_{k=1..n} A036666(k). - Jon Maiga, Nov 28 2018 E.g.f.: (exp(x)*(3 + 63*x + 60*x^2 + 10*x^3) - 3*exp(-x)*(1 - x))/24. - Franck Maminirina Ramaharo, Nov 29 2018 MAPLE A212967:=n->(n+1)*(10*n*(n+2)-3*(-1)^n+3)/24: seq(A212967(n), n=0..100); # Wesley Ivan Hurt, Apr 28 2017 MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w < (Max[w, x, y] - Min[w, x, y]), s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]]; Map[t[#] &, Range[0, 60]] (* A212967 *) Accumulate[Accumulate[Table[n + LCM[n, 2], {n, 0, 60}]]] (* Jon Maiga, Nov 28 2018 *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 3, 10, 26, 50, 89}, 50] (* Vincenzo Librandi, Nov 29 2018 *) PROG (GAP) List([1..45], n->Sum([1..n], k->(10*k*(k-1)+(2*k-1)*(-1)^k+1)/8)); # Muniru A Asiru, Nov 28 2018 (Magma) [(n+1)*(10*n*(n+2) - 3*(-1)^n+3)/24: n in [0..50]]; // Vincenzo Librandi, Nov 29 2018 CROSSREFS Cf. A212959, A212968, A036666. Sequence in context: A190529 A343584 A335970 * A355902 A301410 A333897 Adjacent sequences: A212964 A212965 A212966 * A212968 A212969 A212970 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 02 2012 STATUS approved

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Last modified September 10 16:30 EDT 2024. Contains 375791 sequences. (Running on oeis4.)