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A301926 a(n+3) = a(n) + 24*n + 32, a(0)=0, a(1)=3, a(2)=13. 1

%I

%S 0,3,13,32,59,93,136,187,245,312,387,469,560,659,765,880,1003,1133,

%T 1272,1419,1573,1736,1907,2085,2272,2467,2669,2880,3099,3325,3560,

%U 3803,4053,4312,4579,4853,5136,5427,5725

%N a(n+3) = a(n) + 24*n + 32, a(0)=0, a(1)=3, a(2)=13.

%C Difference table:

%C 0, 3, 13, 32, 59, 93, 136, 187, ...

%C 3, 10, 19, 27, 34, 43, 51, ... = b(n)

%C 7, 9, 8, 7, 9, 8, ... .

%C The sequence of last decimal digits of a(n) has period 15 and contain no 1's, 4's or 8's.

%C a(n) is e(n), hexasection, in A262397(n-1).

%C b(n) mod 9 is of period 9: 3, 1, 1, 0, 7, 7, 6, 4, 4.

%H Colin Barker, <a href="/A301926/b301926.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

%F a(-n) = A262997(n).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

%F Trisections: a(3n) = 4*n*(9*n-1), a(3n+1) = 3 + 20*n + 36*n^2, a(3n+2) = 13 + 44*n + 36*n^2.

%F a(n+15) = a(n) + 40*(22+3*n).

%F G.f.: x*(1 + x)*(3 + 4*x + 5*x^2) / ((1 - x)^3*(1 + x + x^2)). - _Colin Barker_, Jun 20 2018

%t CoefficientList[ Series[ -x (5^3 +9x^2 +7x +3)/(x -1)^3 (x^2 +x +1), {x, 0, 40}], x] (* or *)LinearRecurrence[{2, -1, 1, -2, 1}, {0, 3, 13, 32, 59, 93}, 41] (* _Robert G. Wilson v_, Jun 20 2018 *)

%o (PARI) concat(0, Vec(x*(1 + x)*(3 + 4*x + 5*x^2) / ((1 - x)^3*(1 + x + x^2)) + O(x^40))) \\ _Colin Barker_, Jun 20 2018

%Y Cf. A262997, A262397. A000290, A240438, A016754, A262523 (hexasections). Cf. A130518.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Jun 20 2018

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Last modified May 30 19:04 EDT 2020. Contains 334729 sequences. (Running on oeis4.)