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 A211534 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w = 3x + 3y. 3
 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 3, 3, 6, 6, 6, 10, 10, 10, 15, 15, 15, 21, 21, 21, 28, 28, 28, 36, 36, 36, 45, 45, 45, 55, 55, 55, 66, 66, 66, 78, 78, 78, 91, 91, 91, 105, 105, 105, 120, 120, 120, 136, 136, 136, 153, 153, 153, 171, 171, 171, 190, 190, 190, 210 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS This sequence consists of six 0's followed by triply repeated triangular numbers. For a guide to related sequences, see A211422. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1). FORMULA a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7). a(n) = floor(n/3)*( floor(n/3) - 1 )/2. - Luce ETIENNE, Jul 08 2014 G.f.: -x^6 / ((x-1)^3*(x^2+x+1)^2). - Colin Barker, Feb 17 2015 a(n) = Sum_{i=0..n-3} i*0^(i mod 3)/3. - Wesley Ivan Hurt, Apr 05 2015 MAPLE A211534:=n->floor(n/3)*(floor(n/3)-1)/2: seq(A211534(n), n=0..100); # Wesley Ivan Hurt, Apr 05 2015 MATHEMATICA t[n_] := t[n] = Flatten[Table[-w + 3 x + 3 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]] c[n_] := Count[t[n], 0] t = Table[c[n], {n, 0, 70}] (* A211534 *) FindLinearRecurrence[t] LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {0, 0, 0, 0, 0, 0, 1}, 70] (* Vincenzo Librandi, Apr 05 2015 *) PROG (PARI) concat([0, 0, 0, 0, 0, 0], Vec(-x^6/((x-1)^3*(x^2+x+1)^2) + O(x^100))) \\ Colin Barker, Feb 17 2015 (Magma) [Floor(n/3)*(Floor(n/3)-1)/2 : n in [0..100]]; // Wesley Ivan Hurt, Apr 05 2015 (Magma) [n le 7 select Floor(n/7) else Self(n-1)+2*Self(n-3)-2*Self(n-4)-Self(n-6)+ Self(n-7): n in [1..70]]; // Vincenzo Librandi, Apr 05 2015 CROSSREFS Cf. A211422, A008805 (w = 2x + 2y and doubly repeated triangular numbers). Sequence in context: A281258 A080607 A013322 * A219816 A177821 A166273 Adjacent sequences: A211531 A211532 A211533 * A211535 A211536 A211537 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 15 2012 STATUS approved

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Last modified April 20 00:03 EDT 2024. Contains 371798 sequences. (Running on oeis4.)