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A086601 Triangular numbers + 1 squared.

%I A086601 #26 Apr 10 2022 14:37:51
%S A086601 1,4,16,49,121,256,484,841,1369,2116,3136,4489,6241,8464,11236,14641,
%T A086601 18769,23716,29584,36481,44521,53824,64516,76729,90601,106276,123904,
%U A086601 143641,165649,190096,217156,247009,279841,315844,355216,398161
%N A086601 Triangular numbers + 1 squared.
%C A086601 Also number of n X 2 0..1 arrays with rows and columns unimodal (cf. A223620, column 2). - _Georg Fischer_, Nov 03 2021
%H A086601 Harvey P. Dale, <a href="/A086601/b086601.txt">Table of n, a(n) for n = 0..1000</a>
%H A086601 R. J. Mathar, <a href="/A247158/a247158.pdf">The number of binary nxm matrices with at most k 1's in each row or column</a>, (2014) Table 2 column 2.
%H A086601 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A086601 a(n) = (A000217(n) + 1)^2.
%F A086601 a(n) = (binomial(2+n,2) - binomial(n,1))^2. - _Zerinvary Lajos_, May 30 2006, corrected by _R. J. Mathar_, May 14 2014
%F A086601 a(n) = A000124(n)^2. - _Omar E. Pol_, Oct 30 2007
%F A086601 a(n) = 1 + A061316(n). _Zerinvary Lajos_, Apr 25 2008
%F A086601 G.f.: ( -1+x-6*x^2+x^3-x^4 ) / (x-1)^5. - _R. J. Mathar_, May 14 2014
%e A086601 a(5) = (t(5)+1)^2 = 16^2 = 256.
%p A086601 A086601 := proc(n)
%p A086601     (n+2+n^2)^2 /4 ;
%p A086601 end proc:
%p A086601 seq(A086601(n),n=0..20) ; # _R. J. Mathar_, May 14 2014
%t A086601 (Accumulate[Range[0,40]]+1)^2 (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,4,16,49,121},40] (* _Harvey P. Dale_, Jan 14 2020 *)
%o A086601 (PARI) w=vector(40,i,(t(i)+1)^2)
%Y A086601 Cf. A000124, A000217, A061316, A223620.
%K A086601 nonn,easy
%O A086601 0,2
%A A086601 _Jon Perry_, Jul 23 2003