A211520 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w + 4y = 2x.
0, 0, 0, 1, 2, 3, 5, 7, 10, 12, 16, 19, 24, 27, 33, 37, 44, 48, 56, 61, 70, 75, 85, 91, 102, 108, 120, 127, 140, 147, 161, 169, 184, 192, 208, 217, 234, 243, 261, 271, 290, 300, 320, 331, 352, 363, 385, 397, 420, 432, 456, 469, 494, 507, 533, 547, 574
Offset: 0
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).
Programs
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Haskell
a211520 n = a211520_list !! n a211520_list = 0 : 0 : 0 : scanl1 (+) a178804_list -- Reinhard Zumkeller, Nov 15 2014
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Maple
seq(floor((n-1)^2/4)-floor((n-1)/4)*floor((n+1)/4), n=0..60); # Ridouane Oudra, Nov 21 2024
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Mathematica
t[n_] := t[n] = Flatten[Table[w - 2 x + 4 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]] c[n_] := Count[t[n], 0] t = Table[c[n], {n, 0, 70}] (* this sequence *) FindLinearRecurrence[t] LinearRecurrence[{1,1,-1,1,-1,-1,1},{0,0,0,1,2,3,5},57] (* Ray Chandler, Aug 02 2015 *) -
PARI
{ my(x='x+O('x^66)); concat([0,0,0],Vec( x^3*(1+x+x^3) / ( (1-x)^3*(1+x)^2*(1+x^2) ) ) ) } \\ Joerg Arndt, Apr 02 2017
Formula
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7).
a(n) - a(n-1) = A178804(n-2). - Reinhard Zumkeller, Nov 15 2014
a(n) = (6*n^2-10*n+3+(2*n-7)*(-1)^n-4*(-1)^((2*n-3-(-1)^n)/4))/32. - Luce ETIENNE, Dec 31 2015
a(n) = Sum_{k=1..floor(n/2)} floor((n-k)/2). - Wesley Ivan Hurt, Apr 01 2017
G.f.: x^3 * (1+x+x^3) / ( (1-x)^3*(1+x)^2*(1+x^2) ). - Joerg Arndt, Apr 02 2017
a(n)+a(n-1) = A282513(n-2). - R. J. Mathar, Jun 23 2021
a(n) = floor((n-1)^2/4) - floor((n-1)/4)*floor((n+1)/4). - Ridouane Oudra, Nov 21 2024
Comments