A024598 a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = (odd natural numbers).
1, 3, 14, 22, 55, 73, 140, 172, 285, 335, 506, 578, 819, 917, 1240, 1368, 1785, 1947, 2470, 2670, 3311, 3553, 4324, 4612, 5525, 5863, 6930, 7322, 8555, 9005, 10416, 10928, 12529, 13107, 14910, 15558, 17575, 18297, 20540, 21340, 23821, 24703, 27434, 28402
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
Crossrefs
Cf. A143218.
Programs
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Magma
[(4*n^3 +3*n^2 +2*n -3*n^2*(-1)^n)/12: n in [1..50]]; // G. C. Greubel, Jul 12 2022
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Mathematica
LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,3,14,22,55,73,140},50] (* Harvey P. Dale, Aug 30 2021 *) -
PARI
Vec(x*(3*x^4+2*x^3+8*x^2+2*x+1)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Jan 17 2015
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PARI
odd(n) = 2*n-1; a(n) = sum(j=1, (n+1)\2, odd(j)*odd(n+1-j)); \\ Michel Marcus, Jan 17 2015
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SageMath
[(4*n^3 +3*n^2 +2*n -3*n^2*(-1)^n)/12 for n in (1..50)] # G. C. Greubel, Jul 12 2022
Formula
a(n) = (4*n^3 + 3*n^2 + 2*n - 3*n^2*(-1)^n)/12. - Luce ETIENNE, Jan 17 2015
G.f.: x*(3*x^4 + 2*x^3 + 8*x^2 + 2*x + 1) / ((x-1)^4*(x+1)^3). - Colin Barker, Jan 17 2015
a(n) = Sum_{i=1..n} i * (2*n-i) * (i mod 2). - Wesley Ivan Hurt, Apr 21 2020
E.g.f.: (x/6)*( 2*(3 + 3*x + x^2)*cosh(x) + (3 + 9*x + 2*x^2)*sinh(x) ). - G. C. Greubel, Jul 12 2022
Comments