A235332 - OEIS

%I #24 Nov 13 2024 19:11:00

%S 6,23,49,84,128,181,243,314,394,483,581,688,804,929,1063,1206,1358,

%T 1519,1689,1868,2056,2253,2459,2674,2898,3131,3373,3624,3884,4153,

%U 4431,4718,5014,5319,5633,5956,6288,6629,6979,7338,7706,8083,8469,8864,9268,9681,10103

%N a(n) = n*(9*n + 25)/2 + 6.

%C This is the case d=6 of n*(9*n + 4*d + 1)/2 + d. Other similar sequences are:

%C d=0, A022267;

%C d=1, A064225;

%C d=2, A062123;

%C d=3, A064226;

%C d=4, A022266 (with initial 0);

%C d=5, A178977.

%C First bisection of A235537.

%H Bruno Berselli, <a href="/A235332/b235332.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 G.f.: (6 + 5*x - 2*x^2)/(1 - x)^3.

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

%F 2*a(n) - a(n+1) + 12 = A081267(n).

%F E.g.f.: exp(x)*(12 + 34*x + 9*x^2)/2. - _Elmo R. Oliveira_, Nov 13 2024

%t Table[n (9 n + 25)/2 + 6, {n, 0, 50}]

%t LinearRecurrence[{3,-3,1},{6,23,49},50] (* _Harvey P. Dale_, Feb 12 2022 *)

%o (Magma) [n*(9*n+25)/2+6: n in [0..50]];

%o (PARI) a(n)=n*(9*n+25)/2+6 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A017257 (first differences), A022266, A022267, A062123, A064225, A064226, A081267, A178977, A235537.

%K nonn,easy

%O 0,1

%A _Bruno Berselli_, Jan 22 2014