cp's OEIS Frontend

A226449 a(n) = n*(5*n^2-8*n+5)/2.

%I A226449 #34 Sep 08 2022 08:46:05
%S A226449 0,1,9,39,106,225,411,679,1044,1521,2125,2871,3774,4849,6111,7575,
%T A226449 9256,11169,13329,15751,18450,21441,24739,28359,32316,36625,41301,
%U A226449 46359,51814,57681,63975,70711,77904,85569,93721,102375,111546,121249,131499,142311,153700
%N A226449 a(n) = n*(5*n^2-8*n+5)/2.
%C A226449 Sequences of the type b(m)+m*b(m-1), where b is a polygonal number:
%C A226449 A006003(n) = A000217(n) + n*A000217(n-1)      (b = triangular numbers);
%C A226449 A069778(n) = A000290(n+1) + (n+1)*A000290(n)  (b = square numbers);
%C A226449 A143690(n) = A000326(n+1) + (n+1)*A000326(n)  (b = pentagonal numbers);
%C A226449 A212133(n) = A000384(n) + n*A000384(n-1)      (b = hexagonal numbers);
%C A226449 a(n)       = A000566(n) + n*A000566(n-1)      (b = heptagonal numbers);
%C A226449 A226450(n) = A000567(n) + n*A000567(n-1)      (b = octagonal numbers);
%C A226449 A226451(n) = A001106(n) + n*A001106(n-1)      (b = nonagonal numbers);
%C A226449 A204674(n) = A001107(n+1) + (n+1)*A001107(n)  (b = decagonal numbers).
%H A226449 Bruno Berselli, <a href="/A226449/b226449.txt">Table of n, a(n) for n = 0..1000</a>
%H A226449 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A226449 G.f.: x*(1+5*x+9*x^2)/(1-x)^4.
%F A226449 a(n) - a(-n) = A008531(n) for n>0.
%t A226449 Table[n (5 n^2 - 8 n + 5)/2, {n, 0, 40}]
%t A226449 CoefficientList[Series[x (1 + 5 x + 9 x^2)/(1 - x)^4, {x, 0, 45}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%t A226449 LinearRecurrence[{4,-6,4,-1},{0,1,9,39},50] (* _Harvey P. Dale_, May 19 2017 *)
%o A226449 (Magma) [n*(5*n^2-8*n+5)/2: n in [0..40]];
%o A226449 (Magma) I:=[0,1,9,39]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // _Vincenzo Librandi_, Aug 18 2013
%o A226449 (PARI) a(n)=n*(5*n^2-8*n+5)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A226449 Cf. (see the comment) A000566, A006003, A069778, A143690, A204674, A212133, A226450, A226451.
%K A226449 nonn,easy
%O A226449 0,3
%A A226449 _Bruno Berselli_, Jun 07 2013