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A082562 a(n) = number of values of m such that m can be expressed as the sum of distinct odd numbers with largest odd number in the sum = 2n+1. 2

%I

%S 1,2,4,8,15,24,35,48,63,80,99,120,143,168,195,224,255,288,323,360,399,

%T 440,483,528,575,624,675,728,783,840,899,960,1023,1088,1155,1224,1295,

%U 1368,1443,1520,1599,1680,1763,1848,1935,2024,2115,2208,2303,2400,2499

%N a(n) = number of values of m such that m can be expressed as the sum of distinct odd numbers with largest odd number in the sum = 2n+1.

%C Beginning with the third term, the first differences are the odd positive integers. - _John W. Layman_, Feb 28 2012

%H Colin Barker, <a href="/A082562/b082562.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F For n>2, a(n) = n^2-1. The values of m are all values from 2n+1 to (n+1)^2 except 2n+3 and n^2+2n-1. - _David Wasserman_, Sep 16 2004

%F From _Colin Barker_, Feb 15 2016: (Start)

%F a(n) = n^2-1 for n>2.

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

%F G.f.: (1-x+x^2+x^3+x^4-x^5) / (1-x)^3.

%F (End)

%t Join[{1, 2, 4}, LinearRecurrence[{3, -3, 1}, {8, 15, 24}, 80]] (* and *) Join[{1, 2, 4}, Table[n^2 - 1, {n, 3, 80}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 13 2012 *)

%o (PARI) Vec((1-x+x^2+x^3+x^4-x^5)/(1-x)^3 + O(x^100)) \\ _Colin Barker_, Feb 15 2016

%Y Cf. A082548, A082547.

%K easy,nonn

%O 0,2

%A _Naohiro Nomoto_, May 05 2003

%E More terms from _David Wasserman_, Sep 16 2004

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Last modified September 15 22:10 EDT 2019. Contains 327088 sequences. (Running on oeis4.)